Masatoshi Kokubu

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where Â, B̂, Ĉ, D̂ and h are meromorphic functions on M. Though √ h is a multi-valued function on M, F is well-defined as a PSL(2,C)-valued mapping. A meromorphic map F as in (1.1) is called a null curve if the pull-back of the Killing form by F vanishes, which is equivalent to the condition that the derivative Fz = ∂F/∂z with respect to each complex(More)
After Gálvez, Mart́ınez and Milán discovered a (Weierstrass-type) holomorphic representation formula for flat surfaces in hyperbolic 3-space H, the first, third and fourth authors here gave a framework for complete flat fronts with singularities in H. In the present work we broaden the notion of completeness to weak completeness, and of front to p-front. As(More)
1 Forward These notes are about discrete constant mean curvature surfaces defined by an approach related to integrable systems techniques. We introduce the notion of discrete constant mean curvature surfaces by first introducing properties of smooth constant mean curvature surfaces. We describe the mathematical structure of the smooth surfaces using(More)
In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic 3-space H. Gálvez, Mart́ınez and Milán showed that when the singular set does not accumulate at an end, then the end is asymptotic to a rotationally symmetric flat surface. As a refinement of their result, we show that the asymptotic order (called pitch(More)
We prove several topological properties of linear Weingarten surfaces of Bryant type, as wave fronts in hyperbolic 3-space. For example, we show the orientability of such surfaces, and also co-orientability when they are not flat. Moreover, we show an explicit formula of the non-holomorphic hyperbolic Gauss map via another hyperbolic Gauss map which is(More)