Work

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

Year: 2026

Type: article

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. These theorems imply analogous ones for the flow issuing from relatively compact sets. 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 renormalized p -capacitary potentials to the inverse mean curvature flow with outer obstacle.

Source: Annales de l Institut Henri Poincaré C Analyse Non Linéaire

DOI: 10.4171/aihpc/194

Authors: Luca Benatti, Luciano Mari, Marco Rigoli, Alberto G. Setti, Kai Xu

Institutions: University of Milan, University of Insubria, University of California, Berkeley

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $700

OpenAlex ID: W4417474114

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