arXiv research

We construct a Kruskal-Szekeres-type analytic extension of the Emparan-Reall black ring, and investigate its geometry. We prove that the extension is maximal, globally hyperbolic, and unique within a natural class of extensions. The key to those results is the proof that causal geodesics are either complete, or approac…

The paper examines Reissner-Nordstrøm-de Sitter black holes and their photon sphere.

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.

The Jorge-Meeks $n$-noid ($n\ge 2$) is a complete minimal surface of genus zero with $n$ catenoidal ends in the Euclidean 3-space $\boldsymbol{R}^3$, which has $(2π/n)$-rotation symmetry with respect to its axis. In this paper, we show that the corresponding maximal surface $f_n$ in Lorentz-Minkowski 3-space $\boldsymb…

It is shown that the Kerr-Newman solution, representing charged and rotating stationary black holes, admits analytic extension at the singularity. This extension is obtained by using new coordinates, in which the metric tensor becomes smooth on the singularity ring. On the singularity, the metric is degenerale - its de…

Semi-supervised clustering aims to introduce prior knowledge in the decision process of a clustering algorithm. In this paper, we propose a novel semi-supervised clustering algorithm based on the information-maximization principle. The proposed method is an extension of a previous unsupervised information-maximization …

Analytic linearization and holomorphic extensions for proper groupoids.

Interpolates curves using maximal and minimal surfaces in different spaces.

The paper proposes a new method for dictionary learning using $\ell_p$-norm maximization.

The horizon and geodesic structure of static configurations generated by anisotropic conformal transforms of the Schwarzschild metric is analyzed. We construct the maximal analytic extension of such off--diagonal vacuum metrics and conclude that for small deformations there are different classes of vacuum solutions of …

The refined analytic torsion on compact Riemannian manifolds with boundary has been discussed by B. Vertman and the authors, but these two constructions are completely different. Vertman used a double of de Rham complex consisting of the minimal and maximal closed extensions of a flat connection and the authors used we…

Analytic completeness criterion applied to constant mean curvature surfaces.

We analyze the horizon and geodesic structure of a class of 4D off--diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyz…

Local conditions on boundaries of $C^\infty$ Levi-flat hypersurfaces, in case the boundary is a generic submanifold, are studied. For nontrivial real analytic boundaries we get an extension and uniqueness result, which forces the hypersurface to be real analytic. This allows us to classify all real analytic generic bou…

New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.

A spacetime can be embedded in an enveloping space with all its extensions.

Study on a metric for disk automorphisms with maximal modulus.

The maximal dilatation of certain minimal Lagrangian extensions is bounded by a constant.

The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that it is even inextendible as a Lorentzian manifold with a continuous metric. To capture the obstruction to continuous extens…

The paper classifies extensions of Yang-Mills-type theories, proving maximality and universality are dense properties.

Study optimal consumption with drawdown limits over a fixed time frame.

Solves Merton's investment-consumption problem with certainty equivalent approach.

Two neural network-based mixture models with E-M learning for efficient likelihood computation.

We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated "Arbitrage Pricing Model", we use probabilistic and functional analytic techniques to show the existence of optimal strategies for investors who maximize their expected utility.

Classifies maximal symmetry models of CR dimension 1.

New research proves uniqueness of maximal spacetime boundaries under certain conditions.

The paper provides conditions for smooth CR-manifolds to be CR-diffeomorphic to real-analytic ones.

The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved that if the Cauchy problem has a local solution, this solution has a unique maximal…

The Jacobian of Douady-Earle extension equals 1 only for isometries.

This paper improves tail dependence analysis by introducing a path-based approach.

New proof shows existence of maximal surfaces with special singularities.

Extends functions on symmetric spaces to analytic functions.

Consider a compact Riemannian manifold with boundary. Assume all maximally extended geodesics intersect the boundary at both ends. Then to each maximal geodesic segment one can form a triple consisting of the initial and final vectors of the segment and the length of the segment. The collection of all such triples comp…

Study extends holomorphic forms on noncompact Kahler manifolds.

We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize and become real analytic in space and time. The regularity result is obtained by i…

An analytic extension of the Reissner-Nordstrom solution at and beyond the singularity is presented. The extension is obtained by using new coordinates in which the metric becomes degenerate at $r=0$. The metric is still singular in the new coordinates, but its components become finite and smooth. Using this extension …

Real analytic functions can be extended on manifolds with normal crossings.

Hyperbolicity proven for a specific type of group extension.

We discuss the problem of risk estimation in the classification problem, with specific focus on finding distributions that maximize the confidence intervals of risk estimation. We derived simple analytic approximations for the maximum bias of empirical risk for histogram classifier. We carry out a detailed study on usi…

Variational Gaussian approximates Poisson data for Bayesian inference.

We prove an extension theorem for Kahler currents with analytic singularities in a Kahler class on a complex submanifold of a compact Kahler manifold.

New topological Riemann-Roch theorem for circle fibrations.

Theory proposes neural networks can be initialized for optimal information transmission.

The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing …

The main goal of this survey is to illustrate geometric applications of the Poincaré Lemma to constant mean curvature equations. In 1970, Calabi introduced the duality between minimal graphs in three dimensional Euclidean space and maximal graphs in three dimensional Lorentz space. We construct two extensions of Calabi…

We construct a geometric, real analytic parametrization of the Hitchin component Hit_n(S) of the PSL_n(R)-character variety R_{PSL_n(R)}(S) of a closed surface S. The approach is explicit and constructive. In essence, our parametrization is an extension of Thurston's shear coordinates for the Teichmueller space of a cl…

Paper tackles utility maximization with job-switching and retirement constraints.

This paper tackles resource allocation in multi-user communication networks using a coordinated multi-armed bandit approach.