Minimal sets and classification of singularities

Xiangyu Liang

(University of Warwick)

Event: ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis

Date: Oct 07, 2013, time: 17:50

Abstract. A minimal set is a closed set (in an Euclidean space) whose Hausdorff

measure cannot be decreased by any compactly supported Lipschitz

deformation. This notion was invented by Almgren to give a

reasonable model for Plateau’s problem, which aims at

understanding the behavior of physical objects that admit certain

minimizing property, such as soap films. We shall introduce some

basic definitions, examples and facts about minimal sets and cones, as well as

some results and open problems.