Calculus of Variations and Geometric Measure Theory
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The Heisenberg isoperimetric problem: an anisotropic version

Valentina Franceschi (Dipartimento di Matematica Tullio Levi-Civita, UniversitĂ  di Padova)

created by miranda on 13 Apr 2021

15 apr 2021 -- 16:00   [open in google calendar]

University of Ferrara (On-line)

Abstract.

The Heisenberg group is a classical example of sub-elliptic geometry, which is the framework of a longstanding conjecture formulated by Pansu in 1982 about the shape of isoperimetric sets. In this talk, I will introduce Pansu’s conjecture, discussing the relations between the associated anisotropic perimeter measure and the ambient geometry. I will then present a generalization of the Heisenberg isoperimetric problem allowing for further anisotropies, and I will present a characterization of smooth isoperimetric sets in this framework, based on recent results obtained in collaboration with R.Monti, A.Righini, M.Sigalotti.

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