We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much ...We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.展开更多
In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional...In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.展开更多
For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classica...For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau （i.e., when ： is constant）.展开更多
基金supported by National Natural Science Foundation of China(11301191)supported by MOST(MOST107-2115-M-110-007-MY2)
文摘We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.
基金supported by the National Natural Science Foundation of China under the grant numbers 11126073the Fundamental Research Funds for the Central Universities of SCUT under the grant number 2012ZB0017
文摘In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.
文摘For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau （i.e., when ： is constant）.
