Vol. 307, No. 1, 2020

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Willmore type inequality using monotonicity formulas

Xiaoxiang Chai

Vol. 307 (2020), No. 1, 53–62
Abstract

Simon type monotonicity formulas for the Willmore functional |H|2 in the hyperbolic space n and 𝕊n are obtained. These formulas give a lower bound of Σ|H|2 where Σ2 is any closed surface in 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
Authors
Xiaoxiang Chai
Department of Mathematics
Korea Institute for Advanced Study
Dongdaemun-gu
Seoul
South Korea