对于 $p \gt 1$ 和 $\mathfrak{p} 的静电 $mathfrak{p}$ 容量的 $L_p$ Minkowski 问题\gqslant n^\ast$

Pub Date : 2024-08-07 DOI:10.4310/ajm.2024.v28.n1.a2

Xinbao Lu, Ge Xiong, Jiawei Xiong

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引用次数: 0

摘要

针对 $p \gt 1$ 和 $\mathfrak{p} 的 $L_p$ Minkowski 问题，证明了 $\mathfrak{p}$-capacity 的解的存在性和唯一性。\n$ 时的 $mathfrak{p}$ 容量问题。为此，我们实现了由表面积度量控制的 $\mathfrak{p}$ 容积度量的估计。这项工作是针对 $p \gt 1$ 和 $1 \lt \mathfrak{p}$ 的结果 $\href{https://doi.org/10.4310/jdg/1606964418}{[45]}$ 的续篇。\lt n$.

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The $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity for $p \gt 1$ and $\mathfrak{p} \geqslant n^\ast$

The existence and uniqueness of solutions to the $L_p$ Minkowski problem for $\mathfrak{p}$-capacity for $p \gt 1$ and $\mathfrak{p} \geqslant n$ are proved. For this task, the estimation of $\mathfrak{p}$−capacitary measure controlled below by the surface area measure is achieved. This work is a sequel to the results $\href{https://doi.org/10.4310/jdg/1606964418}{[45]}$ for $p \gt 1$ and $1 \lt \mathfrak{p} \lt n$.

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