The Isoperimetric Problem in Carnot-Caratéodory Spaces

Bruno Pini Mathematical Analysis Seminar

卷:8

Valentina Franceschi¹ 

[1] Inria Saclay (team GECO) and CMAP Ecole Polytechnique;

关键词: isoperimetric problem;    Heisenberg group;    H-type groups;    Grushin spaces;   

DOI  :  10.6092/issn.2240-2829/7799

来源: DOAJ

【 摘 要 】

We present some recent results obtained on the isoperimetric problem in a class of Carnot-Carathéodory spaces, related to the Heisenberg group. This is the framework of Pansu’s conjecture about the shape of isoperimetric sets. Two different approaches are considered. On one hand we describe the isoperimetric problem in Grushin spaces, under a symmetry assumption that depends on the dimension and we provide a classification of isoperimetric sets for special dimensions. On the other hand, we present some results about the isoperimetric problem in a family of Riemannian manifolds approximating the Heisenberg group. In this context we study constant mean curvature surfaces. Inspired by Abresch and Rosenberg techniques on holomorphic quadratic differentials, we classify isoperimetric sets under a topological assumption.

【 授权许可】

Unknown