Translator Disclaimer
July 2020 Evolution of relative Yamabe constant under Ricci Flow
Boris Botvinnik, Peng Lu
Osaka J. Math. 57(3): 679-687 (July 2020).

Abstract

Let $W$ be a manifold with boundary $M$ given together with a conformal class $\bar C$ which restricts to a conformal class $C$ on $M$. Then the relative Yamabe constant $Y_{\bar C}(W,M;C)$ is well-defined. We study the short-time behavior of the relative Yamabe constant $Y_{[\bar g_t]}(W,M;C)$ under the Ricci flow $\bar g_t$ on $W$ with boundary conditions that mean curvature $H_{\bar g_t}\equiv 0$ and $\bar{g}_t|_M\in C = [\bar{g}_0]$. In particular, we show that if the initial metric $\bar{g}_0$ is a Yamabe metric, then, under some natural assumptions, $\left.\frac{d}{dt}\right|_{t=0}Y_{[\bar g_t]}(W,M;C)\geq 0$ and is equal to zero if and only the metric $\bar{g}_0$ is Einstein.

Citation

Download Citation

Boris Botvinnik. Peng Lu. "Evolution of relative Yamabe constant under Ricci Flow." Osaka J. Math. 57 (3) 679 - 687, July 2020.

Information

Published: July 2020
First available in Project Euclid: 13 July 2020

zbMATH: 07224928
MathSciNet: MR4121783

Subjects:
Primary: 53C27, 57R65, 58J05, 58J50

Rights: Copyright © 2020 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
9 PAGES


SHARE
Vol.57 • No. 3 • July 2020
Back to Top