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

Tobias Ekholm

Algebraic & Geometric Topology 6 (2006) 493–512

arXiv: math.GT/0310266


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 8π and we establish a non-injectivity result for local minima.

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immersion, regular homotopy, relatively isotopy tight, sphere eversion, total curvature
Mathematical Subject Classification 2000
Primary: 53C42
Secondary: 53A04, 57R42
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Received: 8 February 2005
Revised: 22 February 2006
Accepted: 12 March 2006
Published: 23 March 2006
Tobias Ekholm
Department of mathematics
Los Angeles CA 90803