In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to b...In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.展开更多
In this paper,we derive an estimate on the potential functions of complete noncompact gradient shrinking solitons of Ricci-harmonic flow,and show that complete noncompact gradient shrinking Ricci-harmonic solitons hav...In this paper,we derive an estimate on the potential functions of complete noncompact gradient shrinking solitons of Ricci-harmonic flow,and show that complete noncompact gradient shrinking Ricci-harmonic solitons have Euclidean volume growth at most.展开更多
In this paper, we explicitly construct some rotationally symmetric gradient pseudo- Kahler-Ricci solitons which depend on some parameters, on some line bundles and other bundles over projective spaces. We also discuss...In this paper, we explicitly construct some rotationally symmetric gradient pseudo- Kahler-Ricci solitons which depend on some parameters, on some line bundles and other bundles over projective spaces. We also discuss the ＂phase change＂ phenomenon caused by the variation of parameters.展开更多
In this paper, we consider the following nonlinear elliptic equation △f^u＋hu^α=0 on the complete smooth metric space （R^n,80, e^-f dv80）, where 80 is the Euclidean metric on R^n and f =丨x丨^2/4. We prove gradien...In this paper, we consider the following nonlinear elliptic equation △f^u＋hu^α=0 on the complete smooth metric space （R^n,80, e^-f dv80）, where 80 is the Euclidean metric on R^n and f =丨x丨^2/4. We prove gradient estimates and Liouville-Type theorems for positive solutions of the above equation.展开更多
In this paper we study on gradient quasi-Einstein solitons with a fourth-order vanishing condition on the Weyl tensor.More precisely,we show that for n≥4,the Cotton tensor of any ndimensional gradient quasi-Einstein ...In this paper we study on gradient quasi-Einstein solitons with a fourth-order vanishing condition on the Weyl tensor.More precisely,we show that for n≥4,the Cotton tensor of any ndimensional gradient quasi-Einstein soliton with fourth order f-divergence free Weyl tensor is flat,if the manifold is compact,or noncompact but the potential function satisfies some growth condition.As corollaries,some local characterization results for the quasi-Einstein metrics are derived.展开更多
On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sh...On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sharp.As an application,we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers.展开更多
In this paper, we derive evolution equation of the integral of the Gauss curvature on an evolving hypersurface. As an application, we obtain a monotone quantity on the level surface of the potential function on a 3-di...In this paper, we derive evolution equation of the integral of the Gauss curvature on an evolving hypersurface. As an application, we obtain a monotone quantity on the level surface of the potential function on a 3-dimensional steady gradient Ricci soliton with positive sectional curvature, and prove that such a soliton is rotationally symmetric outside of a compact set under a curvature decaying assumption. Along the way we will also apply our evolution equation to some other cases.展开更多
基金Supported by the National Natural Science Foundation of China(11771020,12171005).
文摘In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No. 2011JC021)
文摘In this paper,we derive an estimate on the potential functions of complete noncompact gradient shrinking solitons of Ricci-harmonic flow,and show that complete noncompact gradient shrinking Ricci-harmonic solitons have Euclidean volume growth at most.
基金supported by the Natural Science Foundation of Fujian Province(2013J01027)
文摘In this paper, we explicitly construct some rotationally symmetric gradient pseudo- Kahler-Ricci solitons which depend on some parameters, on some line bundles and other bundles over projective spaces. We also discuss the ＂phase change＂ phenomenon caused by the variation of parameters.
文摘In this paper, we consider the following nonlinear elliptic equation △f^u＋hu^α=0 on the complete smooth metric space （R^n,80, e^-f dv80）, where 80 is the Euclidean metric on R^n and f =丨x丨^2/4. We prove gradient estimates and Liouville-Type theorems for positive solutions of the above equation.
文摘In this paper we study on gradient quasi-Einstein solitons with a fourth-order vanishing condition on the Weyl tensor.More precisely,we show that for n≥4,the Cotton tensor of any ndimensional gradient quasi-Einstein soliton with fourth order f-divergence free Weyl tensor is flat,if the manifold is compact,or noncompact but the potential function satisfies some growth condition.As corollaries,some local characterization results for the quasi-Einstein metrics are derived.
基金partially supported by the National Natural Science Foundation of China(11671141)the Natural Science Foundation of Shanghai(17ZR1412800)。
文摘On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sharp.As an application,we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers.
基金Supported by National Natural Science Foundation of China (Grant No. 10926062)Advanced Program for Returned Chinese Overseas Scholars by the Department of Human Resources and Social Security of Zhejiang Province
文摘In this paper, we derive evolution equation of the integral of the Gauss curvature on an evolving hypersurface. As an application, we obtain a monotone quantity on the level surface of the potential function on a 3-dimensional steady gradient Ricci soliton with positive sectional curvature, and prove that such a soliton is rotationally symmetric outside of a compact set under a curvature decaying assumption. Along the way we will also apply our evolution equation to some other cases.
基金supported by the NNSF of China(11071257)Science Foundation of China University of Petroleum,Beijingsupported by Science and Technology Research Projectof Heilongjiang Provincial Department of Education(12511412)
