204 citations · 204 across the 5 of their papers we have counts for
5 papers
An index formula for hemispheres of a -regular convex closed surface in Euclidean -space
Naoya Ando, Masaaki Umehara
Carathéodory's conjecture has long been regarded as one of the central problems in the classical theory of convex surfaces. In this paper, we establish an index formula for hemisph…
Hopf differentials and curvature line flows on time-like CMC surfaces
Naoya Ando, Masaaki Umehara
We investigate the relationship between the Hopf differentials and the curvature line flows on time-like constant mean curvature (CMC) surfaces in Lorentzian 3-space forms. In part…
Examples of entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space via Konderak's formulas
Takeki Komatsu, Masaaki Umehara
Using Konderak's representation formula, we construct an entire zero-mean curvature graph of mixed-type in Lorentz-Minkowski 3-space over a space-like plane, which does not belong…
Cuspidal edges and generalized cuspidal edges in the Lorentz-Minkowski 3-space
T. Fukui, R. Kinoshita, D. Pei +2
It is well-known that every cuspidal edge in the Euclidean space E^3 cannot have a bounded mean curvature function. On the other hand, in the Lorentz-Minkowski space L^3, zero mean…
Singularities of flat fronts in hyperbolic 3-space
Masatoshi Kokubu, Wayne Rossman, Kentaro Saji +2
It is well-known that the unit cotangent bundle of any Riemannian manifold has a canonical contact structure. A surface in a Riemannian 3-manifold is called a (wave) front if it is…