Proper solutions of the 1/H-flow and the Green kernel of the p-Laplacian

2025/12/16 by Benatti, Luca, Mari, Luciano, Rigoli, Marco +2
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.14591

Abstract

We show existence and optimal growth estimate for the weak inverse mean curvature flow issuing from a point, on manifolds with certain curvature and isoperimetric conditions. Some of the results are obtained by proving new decay estimates for the Green kernel of the p-Laplacian which fix a gap in the literature. Additionally, we address the convergence of p-capacitary potentials to the inverse mean curvature flow with outer obstacle.

Citations

• 3-Manifolds with positive scalar curvature and bounded geometry
• Fine properties of nonlinear potentials and a unified perspective on monotonicity formulas
• Inverse mean curvature flow with outer obstacle
• Weak solutions of Anisotropic (and crystalline) inverse mean curvature flow as limits of p-capacitary potentials
• Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature
• Isoperimetry and the properness of weak inverse mean curvature flow
• Inverse mean curvature flow and Ricci-pinched three-manifolds
• Adimensional weighted Sobolev inequalities in PI spaces
• Motion of level sets by inverse anisotropic mean curvature
• Local gradient estimates of p-harmonic functions, 1/H-flow, and an entropy formula
• Weighted Sobolev inequalities and Ricci flat manifolds

Cited by

• The equivalence of isocapacitary notions of mass

Related

• Inverse mean curvature flow with outer obstacle
• Isoperimetry and the properness of weak inverse mean curvature flow
• Weak solutions of Anisotropic (and crystalline) inverse mean curvature flow as limits of p-capacitary potentials
• Asymptotic behaviour of the weak inverse anisotropic mean curvature flow
• Inverse Mean Curvature Flow with Singularities