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math.DG2021
A new family of latitudinally corrugated two-spheres of revolution with simple cut locus
Minoru Tanaka, Toyohiro Akamatsu, Robert Sinclair +1
There are not so many kinds of surface of revolution whose cut locus structure have been determined, although the cut locus structures of very familiar surfaces of revolution (in E…
math.DG2018
The Singular Locus of an Almost Distance Function
Minoru Tanaka
The aim of this article is to generalize the notion of the cut locus and to get the structure theorem for it. For this purpose, we first introduce a class of 1-Lipschitz functions,…
math.DG2012★ 22 cited
The cut locus and distance function from a closed subset of a Finsler manifold
Minoru Tanaka, Sorin V. Sabau
We characterize the differentiable points of the distance function from a closed subset of an arbitrary dimensional Finsler manifold in terms of the number of -segments. In…