Unitarization of Monodromy Representations and Constant Mean Curvature Trinoids in 3-dimensional Space Forms

Constant Mean Curvature Surfaces with Delaunay Ends in 3-dimensional Space Forms

This paper presents a unified treatment of constant mean curvature (cmc) surfaces in the simply-connected 3-dimensional space forms R, S and H in terms of meromorphic loop Lie algebra valued 1-forms. We discuss global issues such as period problems and asymptotic behaviour involved in the construction of cmc surfaces with nontrivial topology. We prove existence of new examples of complete non-s...

‎Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter‎ ‎space or anti-de Sitter space

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Hyperbolic surfaces of $L_1$-2-type

In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

Minimal Disks Bounded by Three Straight Lines in Euclidean Space and Trinoids in Hyperbolic Space

Following Riemann’s idea, we prove the existence of a minimal disk in Euclidean space bounded by three lines in generic position and with three helicoidal ends of angles less than π. In the case of general angles, we prove that there exist at most four such minimal disks, we give a sufficient condition of existence in terms of a system of three equations of degree 2, and we give explicit formul...