Calculus of Variations and Geometric Measure Theory
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Strictly outward minimizing hulls, p-capacities and isoperimetric inequalities

Mattia Fogagnolo

created by malchiodi on 26 Oct 2020

28 oct 2020 -- 17:00   [open in google calendar]

Scuola Normale Superiore, Aula Mancini

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Abstract.

We investigate the notion of strictly outward minimizing hull and prove that under natural geometric assumptions on the ambient manifold the it gives a maximal volume solution to the least area problem with obstacle. Moreover, we recover the value of its area as limit of p-capacities.

Finally, we apply some of these results in order to obtain the sharp isoperimetric inequality on manifolds with nonnegative Ricci curvature and Euclidean volume growth up to dimension 7, up to now known only in dimension 3.

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