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Total variation and Cheeger sets in Gauss space
Authors:Vicent Caselles
Institution:a Departament de Tecnologies de la Informació i les Comunicacions, Universitat Pompeu-Fabra, C/Roc Boronat 138, 08018 Barcelona, Spain
b Dipartimento di Matematica, University of Ferrara, via Machiavelli 35, 44121 Ferrara, Italy
c Dipartimento di Matematica, University of Padova, via Trieste 63, 35121 Padova, Italy
Abstract:The aim of this paper is to study the isoperimetric problem with fixed volume inside convex sets and other related geometric variational problems in the Gauss space, in both the finite and infinite dimensional case. We first study the finite dimensional case, proving the existence of a maximal Cheeger set which is convex inside any bounded convex set. We also prove the uniqueness and convexity of solutions of the isoperimetric problem with fixed volume inside any convex set. Then we extend these results in the context of the abstract Wiener space, and for that we study the total variation denoising problem in this context.
Keywords:Isoperimetric problems  Wiener space  Gaussian measures  Cheeger sets
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