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Surfaces and fronts with harmonic-mean curvature one in hyperbolic three-space
Masatoshi Kokubu
We investigate surfaces with constant harmonic-mean curvature one (HMC-1 surfaces) in hyperbolic three-space. We allow them to have certain kinds of singularities, and discuss some…
Flat fronts in hyperbolic 3-space
Masatoshi Kokubu, Masaaki Umehara, Kotaro Yamada
We shall investigate flat surfaces in hyperbolic 3-space with admissible singularities, called `flat fronts'. An Osserman-type inequality for complete flat fronts is shown. When eq…
An elementary proof of Small's formula for null curves in PSL(2,C) and an analogue for Legendrian curves in PSL(2,C)
Masatoshi Kokubu, Masaaki Umehara, Kotaro Yamada
For null curves in PSL(2,C), there exists a representation formula in terms of two meromorphic functions and their derivatives (Small's formula). In this paper, we give an elementa…
Minimal surfaces that attain equality in the Chern-Osserman inequality
Masatoshi Kokubu, Masaaki Umehara, Kotaro Yamada
In the previous paper, Takahasi and the authors generalized the theory of minimal surfaces in Euclidean n-space to that of surfaces with holomorphic Gauss map in certain class of n…
An analogue of minimal surface theory in SL(n,C)/SU(n)
Masatoshi Kokubu, Masaro Takahashi, Masaaki Umehara +1
We shall discuss the class of surfaces with holomorphic right Gauss maps in non-compact duals of compact semisimple Lie groups (e.g. SL(n,C)/SU(n)), which contains minimal surfaces…