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arXiv · 2211.06939

Monotone quantities of $p$-harmonic functions and their applications

Sven Hirsch·Pengzi Miao·Luen-Fai Tam
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Abstract

We derive local and global monotonic quantities associated to $p$-harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relating the mass of asymptotically flat $3$-manifolds, the $p$-capacity and the Willmore functional of the boundary. As $ p \to 1$, one of the results retrieves a classic relation that the ADM mass dominates the Hawking mass if the surface is area outer-minimizing.

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Sven Hirsch, Pengzi Miao, Luen-Fai Tam. 2022-11-13. Monotone quantities of $p$-harmonic functions and their applications. https://arxiv.org/abs/2211.06939

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