Isodiametric sets in the Heisenberg group

Davide Vittone

(Dip. Matematica, Univ. di Padova)

Event: ERC School on Analysis in Metric Spaces and Geometric Measure Theory

Date: Jan 13, 2011, time: 17:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. In this talk we focus on isodiametric sets in the Heisenberg group, i.e. sets maximizing the volume measure among those with fixed diameter. We first show a Lipschitz regularity result for the boundary of such sets. We are able to solve the isodiametric problem in the restricted class of rotationally invariant sets, where the solution is given by the (Euclidean) convexification of CC-balls. A nonuniqueness
result is also shown. This is joint with G. P. Leonardi and S. Rigot.