Volume 6, issue 1 (2006)

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Regular homotopy and total curvature I: circle immersions into surfaces

Tobias Ekholm

Algebraic & Geometric Topology 6 (2006) 459–492

arXiv: math.GT/0310266

Abstract

We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of spaces of its local minima.

Keywords
circle immersion, geodesic curvature, regular curve, regular homotopy, Riemann surface, total curvature
Mathematical Subject Classification 2000
Primary: 53C42
Secondary: 53A04, 57R42
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Publication
Received: 8 February 2005
Revised: 22 February 2006
Accepted: 12 March 2006
Published: 23 March 2006
Authors
Tobias Ekholm
Department of mathematics
USC
Los Angeles CA 90803
USA