Willmore type inequality using monotonicity formulas

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 ${\mathbb{H}}^n$.

arXiv commentComments welcome, 9 pages

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