The quantitative Hopf theorem and filling volume estimates from below

Luofei Liu

Vol. 231 (2007), No. 2, 445–460

DOI: 10.2140/pjm.2007.231.445

Abstract

Let $V^n$ be a compact, oriented Riemannian manifold and $S^n$ the standard sphere. We study the problem of obtaining upper bounds for the dilatation invariants of maps $V^n\to S^n$ of nonzero degree. The dilatation upper bounds are then used to estimate Gromov’s filling volume from below.

Keywords

dilatation, degree, filling volume

Mathematical Subject Classification 2000

Primary: 53C23, 53C20

Milestones

Received: 20 December 2005

Accepted: 16 May 2006

Published: 1 June 2007