Paper · Apr 29, 2024

Flow by Gauss curvature to the Minkowski problem of p-harmonic measure

Chao Li, Xia Zhao

math.APWider flowsarXiv:2404.18757v2
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Abstract

The Minkowski problem of harmonic measures was first studied by Jerison [19]. Recently, Akman and Mukherjee [1] studied the Minkowski problem corresponding to -harmonic measures on convex domains and generalized Jerison's results. In this paper, we prove the existence of the smooth solution to the Minkowski problem for the -harmonic measure by method of the Gauss curvature flow.

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Submitted
Apr 29, 2024
Last revised
May 6, 2024 (v2)
Subjects
math.AP, math.DG

Comments: 20 pages

Other curvature flowsGauss curvature flow

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Background reading

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Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974) Gauss curvature flow Wider flows Convex hypersurfaces shrink with normal speed a power K^α of their Gauss curvature. Firey proposed it as a model of stones worn by waves; for α>… Start with: Shapes of worn stones (Firey, 1974)