Communications in Analysis and Geometry

Volume 31 (2023)

Number 7

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

Pages: 1655 – 1668

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n7.a2

Authors

Keita Kunikawa (Faculty of Science and Technology, Tokushima University, Tokushima, Japan)

Yohei Sakurai (Department of Mathematics, Saitama University, Saitama, Japan)

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 $W$-functional of Perelman type.

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The first author was supported by JSPS KAKENHI (JP19K14521).

The second author was supported by JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design” (17H06460).

Received 23 October 2020

Accepted 6 July 2021

Published 10 August 2024