#### Volume 6, issue 1 (2006)

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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
##### 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 $8\pi$ 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