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Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 2, pp. 407-438.

We study points of density 1/2 of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density 1/2 is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.

Dans cet article nous étudions la structure de l’ensemble des points avec densité 1/2 pour les ensemble de périmètre fini dans un espace gaussien infini-dimensionnel. Nous démontrons que, comme dans le cas de dimension finie, la mesure de surface est concentrée sur cet ensemble de points. Ici, la définition de points avec densité 1/2 est donnée en utilisant le comportement ponctuel du semigroupe de Ornstein-Uhlembeck.

DOI: 10.5802/afst.1297
Luigi Ambrosio 1; Alessio Figalli 2

1 Scuola Normale Superiore, p.za dei Cavalieri 7, I-56126 Pisa, Italy.
2 The University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin TX 78712, USA
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     author = {Luigi Ambrosio and Alessio Figalli},
     title = {Surface measures and convergence of the {Ornstein-Uhlenbeck} semigroup in {Wiener} spaces},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {407--438},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
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     volume = {Ser. 6, 20},
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Luigi Ambrosio; Alessio Figalli. Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 2, pp. 407-438. doi : 10.5802/afst.1297. https://afst.centre-mersenne.org/articles/10.5802/afst.1297/

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