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Abstract
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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.
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Keywords
circle immersion, geodesic curvature, regular curve,
regular homotopy, Riemann surface, total curvature
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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
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