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Flow by Gauss curvature to the Minkowski problem of p-harmonic measure
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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 $p$-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 $p$-harmonic measure by method of the Gauss curvature flow.
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Cited by 2 Pith papers
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The Lq-Minkowski problem of anisotropic p-torsional rigidity
For every nonzero Borel measure not concentrated in a closed hemisphere, there is a convex body whose Lq anisotropic p-torsional measure equals the measure, up to a constant when 0<q<1.
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Minkowski problem of anisotropic p-torsional rigidity
For the Finsler p-Laplacian torsion problem, a nonzero finite measure is an anisotropic p-torsional measure of a convex body iff its centroid is the origin and it is not concentrated on a closed hemisphere; the log ve...
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