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.
Flow by Gauss curvature to the Minkowski problem of p-harmonic measure
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2025 1verdicts
REJECT 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
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.