Regular homotopy and total curvature II: sphere immersions into 3–space

Ekholm, Tobias

doi:10.2140/agt.2006.6.493

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Regular homotopy and total curvature II: sphere immersions into $3$–space

Tobias Ekholm

Algebraic & Geometric Topology 6 (2006) 493–512

DOI: 10.2140/agt.2006.6.493

arXiv: math.GT/0310266

Abstract

We consider properties of the total curvature functional on the space of 2–sphere immersions into 3–space. We show that the infimum over all sphere eversions of the maximum of the total curvature during an eversion is at most $8 π$ and we establish a non-injectivity result for local minima.

Keywords

immersion, regular homotopy, relatively isotopy tight, sphere eversion, 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)