Poincaré-Wirtinger and linear isoperimetric inequalities on a class of indecomposable integral currents and the Plateau problem in codimension 1 homology classes
本讲教师：DE PAUW Thierry
Abstract：If X is a smooth compact Riemannian manifold then each homology class with integer coefficients admits a mass minimizing integral current representative.This result,due to H. Federer and W.H.Fleming, relies on compactness and the isoperimetric inequality.In this talk I extend this result to a class of singular spaces X. These include semialgebraic sets,sub analytic sets, and more generally sets definable in any o-minimal structure.Simple examples of cusps show that the Euclidean isoperimetric inequality does not hold in this generality and we must settle for a weaker version. This leads to developing a theory of functions of bounded variation defined on integral currents.