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
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
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 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 study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compac...In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.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
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 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 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.
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)
基金supported by NSFC(Grant No.11171143)Zhejiang Provincial Natural Science Foundation of China(Project No.LY13A010009 and LY14A010021)supported by the Fonds National de la Recherche Luxembourg(OPEN Project GEOMREV)
文摘In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.
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.
