24 May 2004
Currents in metric spaces, isoperimetric inequalities, and applications to area minimization problems
Integral currents were introduced by H. Federer and W. H. Fleming in 1960 as a suitable generalization of surfaces in connection with the study of area minimization problems in Euclidean space. L. Ambrosio and B. Kirchheim have recently extended the theory of currents to arbitrary metric spaces. The new theory provides a suitable framework to formulate and study area minimization and isoperimetric problems in metric spaces. The aim of the talk is to discuss such problems for Banach spaces and for spaces with an upper curvature bound in the sense of Alexandrov. We present some techniques which lead to isoperimetric inequalities, solutions to Plateau's problem, and to other results such as the equivalence of flat and weak convergence for integral currents.
- Applied Analysis and Mechanics Seminar