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Recent advances in Geometric Analysis

Critical points of the area of submanifolds of given degree in Carnot manifolds

speaker: Manuel Ritoré (Universidad Granada, Spain)

abstract: Motivated by a visual perception problem, we consider a notion of area for submanifolds of given degree in a Carnot manifold endowed with a Riemannian metric. Particular cases are the length of geodesics in sub-Riemannian manifolds and the perimeter of hypersurfaces in contact sub-Riemannian manifolds. Among others, we consider the relation with the spherical Hausdorff measure associated to the Carnot-Carathéodory distance, the problem of integrability of deformations, the notion of regular submanifolds, and the first variation formula. This is joint work with Gianmarco Giovannardi and Giovanna Citti.

timetable:
Wed 6 Jun, 9:00 - 10:00, Aula Dini
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