Affiliation:
1. Department of Mathematics, University of Toronto, Toronto, Canada
Abstract
We show that for every complete Riemannian surface M diffeomorphic to a sphere with k ≥ 0 holes, there exists a Morse function f : M → ℝ, which is constant on each connected component of the boundary of M and has fibers of length no more than [Formula: see text]. We also show that on every 2-sphere there exists a simple closed curve of length [Formula: see text] subdividing the sphere into two discs of area [Formula: see text].
Publisher
World Scientific Pub Co Pte Lt
Subject
Geometry and Topology,Analysis
Cited by
6 articles.
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