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

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.

The full text of this article is unavailable through your IP address: 13.59.250.115

The first-named author’s research was partially supported by the NSF Grant No. DMS-1926686, and by the IAS School of Mathematics.

The second-named author’s research was partially supported by NSF grant DMS-1906423.

The third-named author’s research was partially supported by Hong Kong RGC General Research Fund #CUHK14301517.

Received 20 November 2022

Received revised 3 April 2023

Accepted 24 April 2023

Published 3 April 2024