When is the Hawking mass monotone under Geometric Flows

TL;DR

This paper investigates the conditions under which the Hawking mass remains monotone during certain geometric flows, specifically demonstrating non-decreasing behavior in Schwarzschild spaces under combined flows.

Contribution

It establishes the monotonicity of Hawking mass along the Hamilton-DeTurck flow coupled with modified mean curvature flow in Schwarzschild spaces, a novel result in geometric flow analysis.

Findings

Hawking mass is monotone non-decreasing under specified flows.

Monotonicity holds for hyperspheres with sufficiently large radius.

Results apply to Schwarzschild spaces with bounded curvature.

Abstract

In this paper, we study the relation of the monotonicity of Hawking Mass and geometric flow problems. We show that along the Hamilton-DeTurck flow with bounded curvature coupled with the modified mean curvature flow, the Hawking mass of the hypersphere with a sufficiently large radius in Schwarzschild spaces is monotone non-decreasing.