3 papers
math.DG2026
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 hemisp…
math.DG2025
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…
math.DG2025
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…