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The \$L_p\$ Minkowski problem for the electrostatic \$\mathfrak{p}\$-capacity
Journal of Differential Geometry  (IF2.688),  Pub Date : 2020-12-03, DOI: 10.4310/jdg/1606964418
Zou Du, Xiong Ge

Existence and uniqueness of the solution to the \$L_p\$ Minkowski problem for the electrostatic \$\mathfrak{p}\$-capacity are proved when \$p \gt 1\$ and \$1 \lt \mathfrak{p} \lt n\$. These results are nonlinear extensions of the very recent solution to the \$L_p\$ Minkowski problem for \$\mathfrak{p}\$-capacity when \$p = 1\$ and \$1 \lt \mathfrak{p} \lt n\$ by Colesanti et al. and Akman et al., and the classical solution to the Minkowski problem for electrostatic capacity when \$p = 1\$ and \$\mathfrak{p} = 2\$ by Jerison.