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- W4380994179 abstract "We derive various sharp upper bounds for the $p$-capacity of a smooth compact set $K$ in the hyperbolic space $mathbb{H}^n$ and the Euclidean space $mathbb{R}^n$. Firstly, using the inverse mean curvature flow, for the mean convex and star-shaped set $K$ in $mathbb{H}^n$, we obtain sharp upper bounds for the $p$-capacity $mathrm{Cap}_p(K)$ in three cases: (1) $ngeq 2$ and $p=2$, (2) $n=2$ and $pgeq 3$, (3) $n=3$ and $1<pleq 3$; Using the unit-speed normal flow, we prove a sharp upper bound for $mathrm{Cap}_p(K)$ of a convex set $K$ in $mathbb{H}^n$ for $ngeq 2$ and $p>1$. Secondly, for the compact set $K$ in $mathbb{R}^3$, using the weak inverse mean curvature flow, we get a sharp upper bound for the $p$-capacity ($1<p<3$) of the set $K$ with connected boundary; Using the inverse anisotropic mean curvature flow, we deduce a sharp upper bound for the anisotropic $p$-capacity ($1<p<3$) of an $F$-mean convex and star-shaped set $K$ in $mathbb{R}^3$." @default.
- W4380994179 created "2023-06-17" @default.
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- W4380994179 date "2023-06-15" @default.
- W4380994179 modified "2023-10-16" @default.
- W4380994179 title "Sharp upper bounds for the capacity in the hyperbolic and Euclidean spaces" @default.
- W4380994179 doi "https://doi.org/10.48550/arxiv.2306.09009" @default.
- W4380994179 hasPublicationYear "2023" @default.
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