A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the sla...A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.展开更多
In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hye...In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces and prove the Hyers-Ulam stability of quadratic p-functional equations associated with the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces.展开更多
Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 fo...Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.展开更多
In this paper, by the definition of almost spirallike mappings of type β and order α and the geometric property of the spirallike mapping of type β, we prove that the generalized Roper-Suffridge extension operator ...In this paper, by the definition of almost spirallike mappings of type β and order α and the geometric property of the spirallike mapping of type β, we prove that the generalized Roper-Suffridge extension operator preserves almost spirallikeness of type β and order α in complex Banach spaces. Key words：展开更多
In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spa...In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.展开更多
A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed...A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.展开更多
In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwahl frame. The geometry of such ma...In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwahl frame. The geometry of such manifolds is controlled by three real invari- ants which live on T＇M： two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular into, rest. Complex Berwald spaces coincide with K/ihler spaces, in the two - dimensional case, We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the Kghler purely Hermitian spaces by the fact K = W=constant and I = 0. For the class of complex Berwald spaces we have K =W = 0. Finally, a classitication of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained.展开更多
We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck form...We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.展开更多
In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fu...In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.展开更多
We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.
We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characteriza...We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.展开更多
This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/...This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/1-r = ＋∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn（C） is given also.展开更多
Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give sev...Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give several characterizations of AUMD spaces.展开更多
This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space P^n（C）.. An example is given to compleme...This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space P^n（C）.. An example is given to complement these results.展开更多
In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of...In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.展开更多
The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property...The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property. The proof is based on inner Hardy martingales introduced here. The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.展开更多
基金This project is supported by the NSFC(10271041)Tianyuan Youth Foundation of Mathematics.
文摘A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.
基金supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(NRF-2012R1A1A2004299)
文摘In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces and prove the Hyers-Ulam stability of quadratic p-functional equations associated with the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces.
基金Supported by the NNSF of China(11971165)the Natural Science Foundation of Zhejiang Province(LY21A010003)。
文摘Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.
文摘In this paper, by the definition of almost spirallike mappings of type β and order α and the geometric property of the spirallike mapping of type β, we prove that the generalized Roper-Suffridge extension operator preserves almost spirallikeness of type β and order α in complex Banach spaces. Key words：
文摘In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.
文摘A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.
文摘In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwahl frame. The geometry of such manifolds is controlled by three real invari- ants which live on T＇M： two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular into, rest. Complex Berwald spaces coincide with K/ihler spaces, in the two - dimensional case, We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the Kghler purely Hermitian spaces by the fact K = W=constant and I = 0. For the class of complex Berwald spaces we have K =W = 0. Finally, a classitication of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained.
基金supported by the Foundation for training Young Teachers in University of Shanghai(ZZegd16003)supported by National Natural Science Foundation of China(11271071,11771087)LMNS,Fudan University
文摘We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.
文摘In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.
文摘We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.
文摘We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.
基金project supported in part by the National Natural Science Foundation of China(10971156)
文摘This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/1-r = ＋∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn（C） is given also.
文摘Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give several characterizations of AUMD spaces.
基金The project supported in part by the National Natural Science Foundation of China (10371091)
文摘This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space P^n（C）.. An example is given to complement these results.
基金The second author was supported by the National Natural Science Foundation of China(11501127)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2014KQNCX068)The third author was supported by the Foundation of Guangzhou Civil Aviation College(18X0428).
文摘In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.
文摘The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property. The proof is based on inner Hardy martingales introduced here. The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.
