Time analyticity for heat equation on gradient shrinking Ricci solitons

TL;DR

This paper proves time analyticity for heat equation solutions on gradient shrinking Ricci solitons with sharp growth conditions, and characterizes backward heat equation solvability in this context.

Contribution

It establishes the time analyticity of heat solutions under sharp growth conditions and provides a criterion for backward heat equation solvability on shrinkers.

Findings

Time analyticity holds for solutions with quadratic exponential growth.

The growth condition for analyticity is proven to be sharp.

A necessary and sufficient condition for backward heat equation solvability is provided.

Abstract

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.