Quasi-isometries and isoperimetric inequalities

We consider the stability of isoperimetric inequalities under quasi-isometries between Riemann surfaces. Kanai observed that quasi-isometries preserve isoperimetric inequalities on complete Riemannian manifolds with finite geometry: positive injectivity radius and Ricci curvature bounded from below (see [2]). In [1], it is shown that the linear isoperimetric inequality is a quasi-isometric invariant for planar Riemann surfaces (genus zero surfaces) with vanishing injectivity radius. Moreover, it is proved that non-linear isoperimetric inequalities can only hold for Riemann surfaces with positive injectivity radius, and hence, by Kanai's observation, preserved by quasi-isometries. In this talk we present an overview on isoperimetric inequalities and give some of the ideas of the proofs of the results cited above.

Gender differences and inequalities in the habits of physical activity of the adult population in Spain

Proyecto I+D+i DEP19801: Gender differences and inequalities in the habits of physical activity of the adult population in Spain

Gender differences and inequalities in the habits of physical activity of the adult population in Spain

Proyecto I+D+i DEP19801: Gender differences and inequalities in the habits of physical activity of the adult population in Spain