Comparison results for capacity
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/43662
comunitat-uji-handle3:10234/43643
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
Comparison results for capacityDate
2012Publisher
Indiana University Mathematics JournalISSN
0022-2518; 1943-5258Type
info:eu-repo/semantics/articlePublisher version
http://dx.doi.org/10.1512/iumj.2012.61.4564Version
info:eu-repo/semantics/acceptedVersionSubject
Abstract
We obtain in this paper bounds for the capacity of a compact set $K$. If $K$ is contained in an $(n+1)$-dimensional Cartan-Hadamard manifold, has smooth boundary, and the principal curvatures of $\partial K$ are larger ... [+]
We obtain in this paper bounds for the capacity of a compact set $K$. If $K$ is contained in an $(n+1)$-dimensional Cartan-Hadamard manifold, has smooth boundary, and the principal curvatures of $\partial K$ are larger than or equal to $H_0>0$, then ${\rm Cap}(K)\geq (n-1)\,H_0{\rm vol}(\partial K)$. When $K$ is contained in an $(n+1)$-dimensional manifold with non-negative Ricci curvature, has smooth boundary, and the mean curvature of $\partial K$ is smaller than or equal to $H_0$, we prove the inequality ${\rm Cap}(K)\leq (n-1)\,H_0{\rm vol}(\partial K)$. In both cases we are able to characterize the equality case. Finally, if $K$ is a convex set in Euclidean space $\mathbb{R}^{n+1}$ which admits a supporting sphere of radius $H_0^{-1}$ at any boundary point, then we prove ${\rm Cap}(K)\geq (n-1)\,H_0\mathcal{H}^n(\partial K)$ and that equality holds for the round sphere of radius $H_0^{-1}$. [-]
Description
postprint de l'autor en arXiv: http://arxiv.org/abs/1012.0487
Is part of
Indiana University Mathematics Journal, Vol. 61 (2), 2012.Related data
http://arxiv.org/abs/1012.0487Rights
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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- INIT_Articles [754]