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- W4286396887 abstract "The notion of strictly outward minimising hull is investigated for open sets of finite perimeter sitting inside a complete noncompact Riemannian manifold. Under natural geometric assumptions on the ambient manifold, the strictly outward minimising hull $Omega^*$ of a set $Omega$ is characterised as a maximal volume solution of the least area problem with obstacle, where the obstacle is the set itself. In the case where $Omega$ has $mathscr{C}^{1, alpha}$-boundary, the area of $partial Omega^*$ is recovered as the limit of the $p$-capacities of $Omega$, as $p to 1^+$. Finally, building on the existence of strictly outward minimising exhaustions, a sharp isoperimetric inequality is deduced on complete noncompact manifolds with nonnegative Ricci curvature, provided $3 leq n leq 7$." @default.
- W4286396887 created "2022-07-22" @default.
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- W4286396887 date "2020-12-17" @default.
- W4286396887 modified "2023-10-16" @default.
- W4286396887 title "Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds" @default.
- W4286396887 doi "https://doi.org/10.48550/arxiv.2012.09490" @default.
- W4286396887 hasPublicationYear "2020" @default.
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