Applications of OMT in proving isoperimetric and Sobolev inequalities

OMT is a powerful method in proving sharp isoperimetric and Sobolev inequalities in the general framework of metric spaces satisfying a curvature-dimension condition ( CD(K,N) spaces). In this talk we focus on the case of CD(0,N) spaces with an asymptotic volume growth at infinity. We shall establish  a sharp isoperimetric inequality in this setting and discuss its consequences. This is a joint work with Alexandru Kristaly.