30 sep 2013
Centro De Giorgi
ERC-School on Geometric Measure Theory and Real Analysis
The lecture is an introduction to Geometric Measure Theory, H-perimeter, minimal surfaces, and to the isoperimetric problem in the Heisenberg group. 1. Introduction. The Heisenberg group and its Lie algebra, Carnot-Caratheodory metric, functional spaces and inequalities. 2. H-perimeter. Sets with finite H-perimeter, blow-up and structure theorems, different notions of surface area, area formulas. 3. Isoperimetric problem. Existence of isoperimetric sets, Pansu conjecture, convex, C2, and symmetric solutions, rearrangements. 4. H-minimal surfaces. Minimal surfaces equations, nonregular minimal surfaces, approximation of minimal boundaries, the regularity problem.