Related papers: Convex plumbings in closed hyperbolic 4-manifolds

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,…

There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…

Locally convex compact immersed hypersurfaces in Finsler-Hadamard manifolds with bounded T-curvature are considered. We prove that such hypersurfaces are embedded as the boundary of convex body under certain conditions on the normal…

We prove that non-compact finite volume hyperbolic 3-manifolds that satisfy a mild cohomological condition (infinitesimal rigidity) admit a family of properly convex deformations of their complete hyperbolic structure where the ends become…

Let $H^4$ denote the hyperbolic four-space. Given a bordered Riemann surface, $M$, we prove that every smooth conformal superminimal immersion $\overline M\to H^4$ can be approximated uniformly on compacts in $M$ by proper conformal…

We obtain some restrictions on the topology of infinite volume hyperbolic manifolds. In particular, for any n and any closed negatively curved manifold M of dimension greater than 2, only finitely many hyperbolic n-manifolds are total…

We prove that for any \e>0, there exists a closed hyperbolic 4-manifold with a closed geodesic of length < \e.

In order to obtain a closed orientable convex projective four-manifold with small positive Euler characteristic, we build an explicit example of convex projective Dehn filling of a cusped hyperbolic four-manifold through a continuous path…

Let M be a closed hyperbolic three manifold. We construct closed surfaces which map by immersions into M so that for each one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding…

Motivated by classical theorems on minimal surface theory in compact hyperbolic three-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic three-manifold of…

We prove that a very general cubic fourfold containing a plane can be embedded into a holomorphic symplectic eightfold as a Lagrangian submanifold. We construct the desired holomorphic symplectic eightfold as a moduli space of Bridgeland…

A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3-manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3-manifold homeomorphic to the interior of M, then the…

Considering an integer $d>0$, we show the existence of convex-cocompactrepresentations of surface groups into SO(4,1) admitting an embedded minimal map withcurvatures in $(-1,1)$ and whose associated hyperbolic 4-manifolds are disk bundles…

We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient…

We show that for certain hyperbolic 3-manifolds, all boundary slopes are slopes of immersed incompressible surfaces, covered by incompressible embeddings in some finite cover. The manifolds include hyperbolic punctured torus bundles and…

We discuss geometric properties of covers of closed hyperbolic manifolds of dimension $n\geq 3$, branched along a totally geodesic codimension two submanifold $\Sigma$. The results are mostly known to the experts but hard to find in the…

We show a generic finiteness result for least area planes in 3-dimensional hyperbolic space. Moreover, we prove that the space of minimal immersions of disk into hyperbolic space is a submanifold of a product bundle over a space of…

We show that every smooth closed oriented four-manifold admits a decomposition into two co- dimension zero submanifolds with common boundary. Each of these submanifolds carries a structure of a symplectic manifold with pseudo-convex…

In this paper we obtain the following results: (1) Any compact Stein surface with boundary embeds naturally into a symplectic Lefschetz fibration over the 2-sphere. (2) There exists a minimal elliptic fibration over the 2-disk, which is not…

Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume…