“Minimal surfaces between Riemannian and sub-Riemannian geometry”
Martedì 14 Gennaio 2025, ore 17:00 - Aula 1BC50 - Simone Verzellesi (Post Doc Università degli Studi di Padova)
Abstract
This seminar aims to be a naive introduction to the theory of minimal surfaces in Riemannian and sub-Riemannian contexts. We begin with a review of some fundamental tools, such as affine connections, the second fundamental form and the mean curvature. The Gauss-Codazzi equations are then presented, along with Simons’ formula in the special case of the Euclidean space. We show how these ideas can be extended to the sub-Riemannian setting, focusing on the Heisenberg group as a leading example. As an application of the Riemannian theory, the Schoen-Simon-Yau curvature estimates are discussed in the Euclidean setting. We conclude by briefly addressing analogous results in the Heisenberg group.
