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arXiv · 1811.05617

Willmore type inequality using monotonicity formulas

Xiaoxiang Chai
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Abstract

Simon type monotonicity formulas for the Willmore functional $\int | \mathbf{H} |^2$ in the hyperbolic space $\mathbb{H}^n$ and $\mathbb{S}^n$ are obtained. The formula gives a lower bound of $\int_{\Sigma} | \mathbf{H} |^2$ where $\Sigma^2$ is any closed surface in $\mathbb{H}^n$.

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Xiaoxiang Chai. 2018-11-14. Willmore type inequality using monotonicity formulas. https://doi.org/10.2140/pjm.2020.307.53

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