Lp Minkowski problem for electrostatic $\mathfrak{p}$-capacity

Abstract

Existence and uniqueness of the solution to the discrete Lp Minkowski problem for $\mathfrak{p}$-capacity are proved when $p\ge 1$ and $1<\mathfrak{p}<n$. For general Lp Minkowski problem for $\mathfrak{p}$-capacity, existence and uniqueness of the solution are given when $p\ge 1$ and $1<\mathfrak{p}\le 2$. These results are non-linear extensions of the very recent solution to the Lp Minkowski problem for $\mathfrak{p}$-capacity when $p=1$ and $1<\mathfrak{p}\le n$ by CNSXYZ, and the classical soution to the Minkowski problem for electrostatic capacity when $p=1$ and $\mathfrak{p}=2$ by Jerison.

38 pages

References in corpus (2)

• The Logarithmic Minkowski Problem
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems