arXiv research

Extended Vaisman theorem to compact spaces with singularities.

We state several sufficient conditions for compact spacelike surface in the3-dimensional de Sitter space to be totally geodesic or spherical.

Neural SDEs model suicide risk with compact state space constraints.

The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in the larger state space.

Proves compactness for timed-metric spaces using new distance and maps.

The paper explores harmonic maps and their properties in symmetric spaces.

I consider compact metric spaces which admit intrinsic isometries to Euclidean d-space. The main result roughly states that the class of these spaces coincides with class of inverse limits of Euclidean d-polyhedra.

Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat Kähler metrics on a minimal Kähler surface whose Kähler classes stay in a compact subset of the interior of the Kähler cone must have a convergent subsequence. As an ap…

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius co…

In this paper two zero-dimensional compact sets with equal topological and fractal dimensions but embedded in Euclidean space by different ways are under study. Diffraction of plane electromagnetic wave propagated and reflected by fractal surfaces is considered for each of these compact sets placed in vacuum. It is obt…

For arbitrary quantizable compact Kaehler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vec…

The paper proves a rigidity theorem for non-compact convex sets in hyperbolic 3-space.

The notion of ideal embeddings was introduced in [B.-Y. Chen, {Strings of Riemannian invariants, inequalities, ideal immersions and their applications.} The Third Pacific Rim Geometry Conference (Seoul, 1996), 7-60, Int. Press, Cambridge, MA, 1998]. Roughly speaking, an ideal embedding (or a best of living) is an isome…

The paper constructs monopole Floer homology for specific 3-manifolds and surfaces.

The main theorem states that any complete connected Riemannian manifold of bounded geometry can be isometrically realized as a leaf with trivial holonomy in a compact Riemannian foliated space.

Existence of Q-processes for Brownian motion on hyperbolic spaces with Poissonian potentials shown.

We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence $X_i$ of Alexandrov spaces with curvature bounded below Gromov-Hausdorff converging to a compact Alexandrov space $X$, $X_i$ is homeomorphic to $X$ for all large $i$.

Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficul…

Heat kernels map RCD spaces to Riemannian manifolds.

For phase-space manifolds which are compact Kaehler manifolds relations between the Berezin-Toeplitz quantization and the quantization with the help of Berezin's coherent states and symbols are studied. First the results on the Berezin-Toeplitz quantization of arbitrary compact Kaehler manifolds due to Bordemann, Meinr…

The classical Cohn-Vossen theorem states that two isometric compact convex surfaces in $\mathbb{R}^{3}$ are congruent. In this short note, we generalize the classical Cohn-Vossen Theorem to higher dimensional surfaces in space form $N^{n+1}(K)$ for $n\ge 2$.

We state some generalizations of a theorem due to G. Darboux, which originally states that a polynomial vector field in the complex plane exhibits a rational first integral and has all its orbits algebraic provided that it exhibits infinitely many algebraic orbits. In this paper, we give an interpretation of this resul…

Study of isometries in Wasserstein spaces under specific conditions.

We introduce imprecise Markov semigroups to handle uncertainty in Markov processes.

The study bounds entanglement entropy for coherent states on Kähler manifolds.

On certain manifolds, the phase which appears in the scalar product of two coherent state vectors is twice the symplectic area of the geodesic triangle determined by the corresponding points on the manifold and the origin of the system of coordinates. This result is proved for compact Hermitian symmetric spaces using t…

The article defines and compares two types of quantizations on compact manifolds.

Geodesically complete affine manifolds are quotients of the Euclidean space through a properly discontinuous action of a subgroup of affine Euclidean transformations. An equivalent definition is that the tangent bundle of such a manifold admits a flat, symmetric and complete connection. If the completeness assumption i…

Signal temporal logic (STL) is an expressive language to specify time-bound real-world robotic tasks and safety specifications. Recently, there has been an interest in learning optimal policies to satisfy STL specifications via reinforcement learning (RL). Learning to satisfy STL specifications often needs a sufficient…

Given a combinatorial description $C$ of a polyhedron having $E$ edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize $C$ is generally not a convex subset of $\mathbb{R}^E$ \cite{DIAZ}. If $C$ has five or more faces, Andreev's Theorem states that the corresponding space of dihedral angle…

In this note we define a distance between two pointed locally integral current spaces. We prove that a sequence of pointed locally integral current spaces converges with respect to this distance if and only if it converges in the sense of Lang-Wenger. This enables us to state the compactness theorem by Lang-Wenger for …

We present a novel cost function for semi-supervised learning of neural networks that encourages compact clustering of the latent space to facilitate separation. The key idea is to dynamically create a graph over embeddings of labeled and unlabeled samples of a training batch to capture underlying structure in feature …

Formula derived for $G_2$-manifolds, showing moduli spaces are incomplete.

We prove that horospheres, hyperspheres and hyperplanes in a hyperbolic space H n , n $\ge$ 3, admit no perturbations with compact support which increase their mean curvature. is is an extension of the analogous result in the Euclidean spaces, due to M. Gromov, which states that a hyperplane in a Euclidean space R n ad…

We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover such a polyhedron is unique, up to global isometries, among convex polyhedra invar…

Paper proves existence of Hadamard states for Maxwell equations.

The paper extends Gray's result to quaternion-Kähler manifolds.

DCAE learns compact latent representations for one-class novelty detection.

We explore Deep Reinforcement Learning in a parameterized action space. Specifically, we investigate how to achieve sample-efficient end-to-end training in these tasks. We propose a new compact architecture for the tasks where the parameter policy is conditioned on the output of the discrete action policy. We also prop…

We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the t…

Any two compact, complete, one-dimensional geodesic spaces with identical marked length spectrum have isometric $π_1$-hull. The present version contains errors, notably in Lemmas 2.2 and 2.3 (path cancellations can be more complicated), which then propagate through the paper. The main result is correct as stated, and a…

New manifolds help understand group actions on complex chains.

We show that non-degenerate hyperquadrics in R^{n+2} admit no skew branes. Stated more traditionally, a compact codimension-one immersed submanifold of a non-degenerate hyperquadric of euclidean space must have parallel tangent spaces at two distinct points. Similar results have been proven by others, but (except for e…

We find a Sasaki-Einstein metric from a CFT state in AdS5.

Freedman proposes a family of Hamiltonians $H_{0,l}$ which define quantum loop gas models on any celluated compact surface. We study the simplest nontrivial cases: celluations of the torus. Our numerical data support Freedman's conjecture, but the conjectured space of ground states does not come out in full.

We give positive answers for questions by Berestovskii. Namely, we prove that every bijection of locally compact geodesically complete and connected at infinity CAT(0)-space $X$ onto itself preserving some fixed distance or satellite relations is an isometry of this space. The proof of this theorem is based on another …

A classical result of Sampson and Schoen-Yau in 1978 states that every diffeomorphism between compact hyperbolic Riemann surfaces is homotopic to an harmonic diffeomorphism. As conjectured by Schoen in 1993 and partially proved by Wan in 1992 and Tam-Wan in 1995, we prove in this article that this theorem generalizes t…

For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves holomorphic sections of line bundles.