Monotone quantities of p-harmonic functions and their applications

2022/11/13 by Sven Hirsch, Pengzi Miao, Hirsch, Sven +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2211.06939

openalex publication_date 2022/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 → 1, one of the results retrieves a classic relation that the ADM mass dominates the Hawking mass if the surface is area outer-minimizing.

Related

• Monotone Quantities for p-Harmonic functions and the Sharp p-Penrose inequality
• New monotonicity for p-capacitary functions in 3-manifolds with nonnegative scalar curvature
• Monotonicity of harmonic functions on 3-manifolds with an asymptotically flat end
• ADM mass, area and capacity in asymptotically flat 3-manifolds with nonnegative scalar curvature
• Fine properties of nonlinear potentials and a unified perspective on monotonicity formulas