Perimeter as relaxed Minkowski content in metric measure spaces
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Publication:515917
DOI10.1016/j.na.2016.03.010zbMath1359.28002arXiv1603.08412OpenAlexW2963621692MaRDI QIDQ515917
Nicola Gigli, Luigi Ambrosio, Simone Di Marino
Publication date: 17 March 2017
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.08412
Length, area, volume, other geometric measure theory (28A75) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items (17)
On BV functions and essentially bounded divergence-measure fields in metric spaces ⋮ Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds ⋮ Stability of eigenvalues and observable diameter in RCD\((1, \infty)\) spaces ⋮ Isoperimetric inequality in noncompact 𝖬𝖢𝖯 spaces ⋮ Quasiconformal mappings and curvatures on metric measure spaces ⋮ The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces ⋮ The Cheeger cut and Cheeger problem in metric measure spaces ⋮ The metric measure boundary of spaces with Ricci curvature bounded below ⋮ Sharp log-Sobolev inequalities in \(\mathsf{CD}(0, N)\) spaces with applications ⋮ The Cheeger problem in abstract measure spaces ⋮ Strong approximation of sets of finite perimeter in metric spaces ⋮ Local isoperimetric inequalities in metric measure spaces verifying measure contraction property ⋮ Rigidity of some functional inequalities on RCD spaces ⋮ The equality case in Cheeger's and Buser's inequalities on \(\mathsf{RCD}\) spaces ⋮ Notions of Dirichlet problem for functions of least gradient in metric measure spaces ⋮ Quantitative estimates for the Bakry-Ledoux isoperimetric inequality ⋮ On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
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