相关论文: Compact Hyperbolic Manifolds as Internal Worlds

The space forms, the complex hyperbolic spaces and the quaternionic hyperbolic spaces are characterized as the harmonic manifolds with specific radial eigenfunctions of the Laplacian.

In this article, we consider a complete, non-compact almost Hermitian manifold whose curvature is asymptotic to that of the complex hyperbolic plane. Under natural geometric conditions, we show that such a manifold arises as the interior of…

The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…

In a variety of settings we provide a method for decomposing a 3-manifold $M$ into pieces. When the pieces have the appropriate type of hyperbolicity, then the manifold $M$ is hyperbolic and its volume is bounded below by the sum of the…

This paper is a continuation of our paper about boundary rigidity and filling minimality of metrics close to flat ones. We show that compact regions close to a hyperbolic one are boundary distance rigid and strict minimal fillings. We also…

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…

Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold…

We show that any compact orientable hyperbolic 3-cone-manifold with cone angle at most \pi can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the local…

It is shown that moduli spaces of complete families of compact complex hypersurfaces in complex manifolds often come equipped canonically with projective structures satisfying some natural integrability conditions.

We prove that there are infinitely many pairwise non-commensurable hyperbolic $n$-manifolds that have the same ambient group and trace ring, for any $n \geq 3$. The manifolds can be chosen compact if $n \geq 4$.

We describe several methods to construct minimal foliations by hyperbolic surfaces on closed 3-manifolds, and discuss the properties of the examples thus obtained.

We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we…

We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…

We compare the volume of a hyperbolic 3-manifold $M$ of finite volume and the complexity of its fundamental group.

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.

We present a simple algorithm for finding eigenmodes of the Laplacian for arbitrary compact hyperbolic 3-manifolds. We apply our algorithm to a sample of twelve manifolds and generate a list of the lowest eigenvalues. We also display a…

In this paper, we study the intrinsic mean curvature flow on certain closed spacelike manifolds, and prove the existence of hyperbolic structures on them.

We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed point sets are nonseparating.

It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases