Willmore type inequality using monotonicity formulas

Xiaoxiang Chai

Vol. 307 (2020), No. 1, 53–62

DOI: 10.2140/pjm.2020.307.53

Abstract

Simon type monotonicity formulas for the Willmore functional $\int \; <!--nolimits-->|H{|}^2$ in the hyperbolic space ${ℍ}^n$ and ${\mathbb{𝕊}}^n$ are obtained. These formulas give a lower bound of ${\int \; <!--nolimits-->}_{\Sigma }|H{|}^2$ where ${\Sigma }^2$ is any closed surface in ${ℍ}^n$.

Keywords

Willmore inequality, monotonicity formula, hyperbolic space

Mathematical Subject Classification 2010

Primary: 53A30, 53B21

Milestones

Received: 24 November 2018

Revised: 30 March 2019

Accepted: 4 February 2020

Published: 8 August 2020