Abstract.
We establish, by simple semigroup arguments, a Lévy–Gromov isoperimetric inequality for the invariant measure of an infinite dimensional diffusion generator of positive curvature with isoperimetric model the Gaussian measure. This produces in particular a new proof of the Gaussian isoperimetric inequality. This isoperimetric inequality strengthens the classical logarithmic Sobolev inequality in this context. A local version for the heat kernel measures is also proved, which may then be extended into an isoperimetric inequality for the Wiener measure on the paths of a Riemannian manifold with bounded Ricci curvature.
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Oblatum 19-VI-1995
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Bakry, D., Ledoux, M. Lévy–Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator. Invent math 123, 259–281 (1996). https://doi.org/10.1007/s002220050026
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DOI: https://doi.org/10.1007/s002220050026