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

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.