Filling inequalities do not depend on topology

2007/06/19 by Michael Brunnbauer, Brunnbauer, Michael
Mathematics · #53C20 #53C23 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:53C20 #msc:53C23

paper · pdf · doi:10.48550/arxiv.0706.2790

13 pages. Corrected some minor errors. To appear in Journal für die reine und angewandte Mathematik (Crelle's Journal)

arxiv created 2008/04/24 · arxiv updated 2009/12/01

Abstract

Gromov's universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contrasts with the analogous situation for the optimal systolic inequality, which does depend on the manifold.

Related

• A short proof of Gromov's filling inequality
• A local systolic inequality and Gromov's filling area conjecture
• Upper and lower bounds on the filling radius
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