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arXiv · 1606.02489

Monotonicity formulas in potential theory

Virginia Agostiniani·Lorenzo Mazzieri
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Abstract

Using the electrostatic potential $u$ due to a uniformly charged body $\Omega\subset\mathbb R^n$, $n\geq 3$, we introduce a family of monotone quantities associated with the level set flow of $u$. The derived monotonicity formulas are exploited to deduce a new quantitative version of the classical Willmore inequality.

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Virginia Agostiniani, Lorenzo Mazzieri. 2016-06-08. Monotonicity formulas in potential theory. https://arxiv.org/abs/1606.02489

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