Regular homotopy and total curvature I: circle immersions into surfaces

Ekholm, Tobias

doi:10.2140/agt.2006.6.459

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Regular homotopy and total curvature I: circle immersions into surfaces

Tobias Ekholm

Algebraic & Geometric Topology 6 (2006) 459–492

DOI: 10.2140/agt.2006.6.459

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

Volume 6, issue 1 (2006)