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arXiv · 2605.31202

Mass-$p$-Capacity Inequalities in Asymptotically Flat Half-Spaces

Chao Xia·Jiabin Yin·Xingjian Zhou
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Abstract

In this paper, we establish general monotone quantities and sharp mass-capacity inequalities related to $p$-capacitary functions in $3$-dimensional asymptotically flat half-spaces of simple topology with nonnegative scalar curvature and nonnegative boundary mean curvature. These inequalities attain equality on a Schwarzschild half-space outside a rotationally symmetric half sphere.

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Chao Xia, Jiabin Yin, Xingjian Zhou. 2026-05-29. Mass-$p$-Capacity Inequalities in Asymptotically Flat Half-Spaces. https://arxiv.org/abs/2605.31202

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