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 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.
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.
