Liouville theorem for heat equation along ancient super Ricci flow via reduced geometry

TL;DR

This paper establishes a Liouville theorem for the heat equation along ancient super Ricci flows, utilizing Perelman's reduced distance to formulate growth conditions, advancing understanding of geometric analysis in evolving manifolds.

Contribution

It introduces a Liouville theorem for heat equations on ancient super Ricci flows based on reduced geometry and growth conditions, extending previous results in geometric analysis.

Findings

Liouville theorem for heat equation along ancient super Ricci flow

Use of Perelman's reduced distance in growth conditions

Advancement in understanding heat equations on evolving manifolds

Abstract

The aim of this article is to provide a Liouville theorem for heat equation along ancient super Ricci flow. We formulate such a Liouville theorem under a growth condition concerning Perelman's reduced distance.