Backward Uniqueness of Extrinsic Geometric Flow in general ambient manifolds

TL;DR

This paper establishes backward uniqueness theorems for various extrinsic geometric flows of hypersurfaces in general ambient Riemannian manifolds, covering flows like mean curvature and Gauss curvature flows.

Contribution

It proves backward uniqueness results for a broad class of extrinsic geometric flows in general ambient manifolds, extending previous results to non-compact hypersurfaces.

Findings

Backward uniqueness holds for mean curvature flow.

Backward uniqueness applies to inverse mean curvature flow.

Results include flows like Gauss curvature flow.

Abstract

In this paper we prove two backward uniqueness theorems for extrinsic geometric flow of possibly non-compact hypersurfaces in general ambient complete Riemannian manifolds. These are applicable to a wide range of extrinsic geometric flow, including the mean curvature flow, inverse mean curvature flow, Gauss curvature flow and so on.