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

Luca Benatti; Luciano Mari; Marco Rigoli; Alberto G. Setti; Kai Xu

Paper

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

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

-Laplacian which fix a gap in the literature. Additionally, we address the convergence of

-capacitary potentials to the inverse mean curvature flow with outer obstacle.