#### 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 $\int |H{|}^{2}$ in the hyperbolic space ${ℍ}^{n}$ and ${\mathbb{𝕊}}^{n}$ are obtained. These formulas give a lower bound of ${\int }_{\Sigma }|H{|}^{2}$ where ${\Sigma }^{2}$ is any closed surface in ${ℍ}^{n}$.

##### Keywords
Willmore inequality, monotonicity formula, hyperbolic space
##### Mathematical Subject Classification 2010
Primary: 53A30, 53B21