Minimax Eversion

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, minimax eversions are a class of sphere eversions, constructed by using half-way models. It is a variational method, and consists of special homotopies (they are shortest paths with respect to Willmore energy); contrast with Thurston's corrugations, which are generic. The original method of half-way models was not optimal: the regular homotopies passed through the midway models, but the path from the round sphere to the midway model was constructed by hand, and was not gradient ascent/descent. Eversions via half-way models are called tobacco-pouch eversions by Francis and Morin.