22 citations · 58 across the 16 of their papers we have counts for
16 papers
Delta-convex structure of the singular set of distance functions
Tatsuya Miura, Minoru Tanaka
For the distance function from any closed subset of any complete Finsler manifold, we prove that the singular set is equal to a countable union of delta-convex hypersurfaces up to…
Generalized von Mangoldt surfaces of revolution and asymmetric two-spheres of revolution with simple cut locus structure
Minoru Tanaka, Toyohiro Akamatsu, Robert Sinclair +1
It was known that if the Gaussian curvature function along each meridian on a surface of revolution is decreasing, then the cut locus of each point of $θ^{…
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…
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,…
Differentiable sphere theorems whose comparison spaces are standard spheres or exotic ones
Kei Kondo, Minoru Tanaka
We show that for an arbitrarily given closed Riemannian manifold admitting a point with a single cut point, every closed Riemannian manifold admitting a point $q…
Approximations of Lipschitz maps via immersions and differentiable exotic sphere theorems
Kei Kondo, Minoru Tanaka
As our main theorem, we prove that a Lipschitz map from a compact Riemannian manifold into a Riemannian manifold admits a smooth approximation via immersions if the map has…