相关论文: On the Calabi-Yau problem for maximal surfaces in …

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…

We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the…

In this paper, we consider a Minkowski inequality for a domain supported on any umbilical hypersurface with free boundary in space forms. We generalize the main result in \cite{Xia} into free boundary case and obtain a free boundary version…

We prove four results towards a description, in terms of the null support function, of the set of isometric embeddings of the hyperbolic plane into Minkowski 3-space. We show that for sufficiently tame null support function, the…

In this paper we establish some parabolicity criteria for maximal surfaces immersed into a Lorentzian product space of the form $M^2\times\mathbb{R}_1$, where $M^2$ is a connected Riemannian surface with non-negative Gaussian curvature and…

In this article spacelike hypersurfaces immersed in twisted product spacetimes $I\times_f F$ with complete fiber are studied. Several conditions ensuring global hyperbolicity are presented, as well as a relation that needs to hold on each…

The aim of this paper is to classify mildly singular Calabi-Yau threefolds fibred in low-degree weighted K3 surfaces and embedded as anticanonical hypersurfaces in weighted scrolls, extending results of Mullet. We also study projective…

In part I of this paper we constructed certain fibered Calabi-Yaus by a quotient construction in the context of weighted hypersurfaces. In this paper look at the case of K3 fibrations more closely and study the singular fibers which occur.…

Some analysis on the Lorentzian distance in a spacetime with controlled sectional (or Ricci) curvatures is done. In particular, we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the Omori-Yau…

We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in $\mathbb R^3$ with bounded image. The analogous result holds for holomorphic immersions…

We prove a Minkowski type inequality for weakly mean convex and star-shaped hypersurfaces in warped cylinders which are asymptotically flat or hyperbolic. In particular, we show that this sharp inequality holds for outward minimizing…

In this paper we study lightlike surfaces of Minkowski 3- space such that they have degenerate or non-degenerate planar normal sections. We first show that every lightlike surface of Minkowski $3-$ space has degenerate planar normal…

The existence of embedded minimal surfaces in non-compact 3-manifolds remains a largely unresolved and challenging problem in geometry. In this paper, we address several open cases regarding the existence of finite-area, embedded, complete,…

In this paper we prove that any immersed stable capillary hypersurfaces in a ball in space forms are totally umbilical. This solves completely a long-standing open problem. In the proof one of crucial ingredients is a new Minkowski type…

In this paper we classify a kind of special Calabi hypersurfaces with negative constant sectional curvature in Calabi affine geometry. Meanwhile, we find a class of new Euclidean complete and Calabi complete affine hypersurfaces, which…

We consider the problem $F=f(\nu)$ for strictly convex, closed hypersurfaces in hyperbolic space and solve it for curvature functions $F$ the inverses of which are of class $(K^*)$.

We investigate complete minimal submanifolds $f\colon M^3\to\Hy^n$ in hyperbolic space with index of relative nullity at least one at any point. The case when the ambient space is either the Euclidean space or the round sphere was already…

In this paper, we establish monotonicity formulas for capillary surfaces in the half-space $\mathbb{R}^3_+$ and in the unit ball $\mathbb{B}^3$ and extend the result of Volkmann (Comm. Anal. Geom.24(2016), no.1, 195~221.…

In this paper we study surfaces with minimal potential energy under gravitational forces, called singular minimal surfaces. We prove that a singular minimal ruled surface in a Euclidean $3-$space is cylindrical, in particular as an…

Following [1] and [2], we discuss the Picard-Fuchs equation for the super Landau-Ginsburg mirror to the super-Calabi-Yau in WCP^(3|2)[1,1,1,3|1,5], (using techniques of [3,4]) Meijer basis of solutions and monodromies (at 0,1 and \infty) in…