Lower bounds for codimension-1 measure in metric manifolds

• Kyle Kinneberg ^[1]
  1. [1] Rice University

     Rice University

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 3, 2018, págs. 1103-1118
• Idioma: inglés
• DOI: 10.4171/RMI/1018
• Texto completo no disponible (Saber más ...)
• Resumen

  • We establish Euclidean-type lower bounds for the codimen\-sion-1 Hausdorff measure of sets that separate points in doubling and linearly locally contractible metric manifolds. This gives a quantitative topological isoperimetric inequality in the setting of metric manifolds, in the sense that lower bounds for the codimension-1 measure of a set depend not on some notion of filling or volume but rather on in-radii of complementary components. As a consequence, we show that balls in a closed, connected, doubling,