Calculus of Variations and Geometric Measure Theory

G. Alberti

Geometric Measure Theory

created by alberti on 06 Mar 2007


Published Paper

Inserted: 6 mar 2007

Year: 2005

published in the Encyclopedia of Mathematical Physics (J.-P. Francoise et al. eds.)


The aim of this short note is to give a brief, self-contained introduction to that part of Geometric Measure Theory which is more directly related to the Calculus of Variations, namely the theory of currents and its applications to the solution of Plateau problem.

Keywords: Rectifiable sets, Hausdorff measure, Hausdorff dimension, self-similar fractals, area formula, rectifiable and integral currents, mass-minimizing currents, minimal surfaces, Plateau problem