Hamilton type entropy formula along the Ricci flow on surfaces with boundary

TL;DR

This paper introduces a Hamilton type entropy formula that remains monotonic along Ricci flow on surfaces with boundary, linking it to Perelman's $ ext{W}$-functional, advancing understanding of geometric flows with boundary conditions.

Contribution

It establishes a new monotonicity formula for Hamilton type entropy on surfaces with boundary and explores its relation to Perelman's $ ext{W}$-functional.

Findings

Proved monotonicity of Hamilton type entropy under Ricci flow on surfaces with boundary.

Connected the entropy functional to Perelman's $ ext{W}$-functional.

Provided insights into geometric analysis of surfaces with boundary.

Abstract

In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy functional and the $\mathcal{W}$-functional of Perelman type.