Annales de l Institut Henri Poincaré C Analyse Non Linéaire· 2026Q1
Proper solutions of the $1/H$-flow and the Green kernel of the $p$-Laplacian
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- 2026year
Short summary
New decay estimates for the Green kernel of the p-Laplacian are proven, fixing a literature gap and enabling existence theorems for weak inverse mean curvature flow.
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Key points
- Existence and optimal growth estimates for weak inverse mean curvature flow from a point are proven.
- New decay estimates for the Green kernel of the p-Laplacian are established, correcting a literature gap.
- Results are extended to inverse mean curvature flows originating from relatively compact sets.
- Convergence of renormalized p-capacitary potentials to inverse mean curvature flow with an outer obstacle is addressed.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Annales de l Institut Henri Poincaré C Analyse Non Linéaire, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics