相关论文: The moduli space of embedded singly periodic maxim…

We show that a complete embedded maximal surface in the 3-dimensional Lorentz-Minkowski space $L^3$ with a finite number of singularities is, up to a Lorentzian isometry, an entire graph over any spacelike plane asymptotic to a vertical…

A maximal surface $\sb$ with isolated singularities in a complete flat Lorentzian 3-manifold $\N$ is said to be entire if it lifts to a (periodic) entire multigraph $\tilde{\sb}$ in $\l^3.$ In addition, $\sb$ is called of finite type if it…

Utilizing the Weierstrass representation for embedded doubly periodic minimal surfaces with parallel ends, we construct entire singly periodic graphs of spacelike maximal surfaces with isolated cone-like singularities in the…

The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence,…

We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space $\Mk$ of…

In this paper we deal with the uniqueness of the Lorentzian helicoid and Enneper's surface among properly embedded maximal surfaces with lightlike boundary of mirror symmetry in the Lorentz-Minkowski space L3.

Until now, the only known maximal surfaces in Minkowski 3-space of finite topology with compact singular set and without branch points were either genus zero or genus one, or came from a correspondence with minimal surfaces in Euclidean…

We give a different formulation for describing maximal surfaces in Lorentz-Minkowski space, $\mathbb{L}^3$, using the identification of $\mathbb L^3$ with $\mathbb C\times \mathbb R$. Further we give a different proof for the singular…

We show that to every maximal surface with conelike singularities in Lorentz-Minkowski space $\mathbb{L}^3$ that can be locally represented as the graph of a smooth function, there exists a corresponding timelike minimal surface in…

We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de…

By a result of W.~P. Thurston, the moduli space of flat metrics on the sphere with $n$ cone singularities of prescribed positive curvatures is a complex hyperbolic orbifold of dimension $n-3$. The Hermitian form comes from the area of the…

We shall investigate maximal surfaces in Minkowski 3-space with singularities. Although the plane is the only complete maximal surface without singular points, there are many other complete maximal surfaces with singularities and we show…

In this paper, we study the relation of the sign of the Gaussian and mean curvature of modular surfaces in Lorentz-Minkowski $3$-space to the zeroes of the associated complex analytic functions and its derivatives. Further, we completely…

In this paper we realize the moduli spaces of cubic fourfolds with specified automorphism groups as arithmetic quotients of complex hyperbolic balls or type IV symmetric domains, and study their compactifications. Our results mainly depend…

We study singularities of spacelike, constant (non-zero) mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space $L^3$. We show how to solve the singular Bj\"orling problem for such surfaces, which is stated as follows: given a real…

We prove that the moduli space of empty real Enriques surfaces (and, thus, the moduli space of compact orientable 4-dimensional Einstein manifolds whose universal covering is a K3-surface and \pi_1(E) = Z/2 x Z/2) is connected. The proof is…

We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.

We prove that a maximal surface in Lorentz-Minkowski space $\Bbb L^3$ can be extended analytically along its boundary if the boundary lies in a plane meeting the surface at a constant angle.

This article introduces a universal moduli space for the set whose archetypal element is a pair that consists of a metric and second fundamental form from a compact, oriented, positive genus minimal surface in some hyperbolic 3-manifold.…

A timelike minimal surface in Minkowski 3-space is a surface whose induced metric is Lorentzian and with vanishing mean curvature. Such surfaces have many kinds of singularities. In this paper, we prove existence and non-existence theorems…