arXiv research

We show that for a strongly convergent sequence of geometrically finite Kleinian groups with geometrically finite limit, the Cannon-Thurston maps of limit sets converge uniformly. If however the algebraic and geometric limits differ, as in the well known examples due to Kerckhoff and Thurston, then provided the geometr…

Geometrically infinite Kleinain groups have nonconical limit sets with the cardinality of the continuum. In this paper, we construct a geometrically infinite Fuchsian group such that the Hausdorff dimension of the nonconical limit set equals zero. For finitely generated, geometrically infinite Kleinian groups, we prove…

The paper characterizes arithmetic metrics in coarsely geometric settings.

We introduce the notion of partial presimplicial set and construct its geometric realization. We show that any semiadequate diagram yields a partial presimplicial set leading to a geometric realization of the almost-extreme Khovanov homology of the diagram. We give a concrete formula for the homotopy type of this geome…

The paper extends geometric inequalities for nearly spherical sets in various space forms.

The paper establishes pressure gaps for manifolds with flat subtori singularities.

Deep learning models complex multivariate extremes using geometric shapes.

Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.

Equivariant networks improve geometric prediction without scalar approximations.

The paper extends geometric inequalities from Euclidean space to Riemannian manifolds.

Study shows continuity and geometric regularity of Kähler-Ricci flow blow-up limits.

Let $U(\boldsymbol r),\boldsymbol r\inΩ\subset \mathbb R^2$ be a harmonic function that solves an exterior Dirichlet problem. If all the level sets of $U(\boldsymbol r),\boldsymbol r\inΩ$ are smooth Jordan curves, then there are several geometric inequalities that correlate the curvature $κ(\boldsymbol r)$ with the ma…

Extends geometric approach to model non-stationary extremal dependence.

New method proves length spectrum rigidity in various geometric settings.

Researchers geometrically define asymptotic coordinates in General Relativity.

Study continuity of limit sets in symmetric spaces.

Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.

We give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.

The horocyclic flow on geometrically infinite surfaces shows recurrent irregular orbits or non-minimal closures.

Prove asymptotics of geometric flows using algebro-geometric methods.

We study geometric realization questions of curvature in the affine, Riemannian, almost Hermitian, almost para Hermitian, almost hyper Hermitian, almost hyper para Hermitian, Hermitian, and para Hermitian settings. We also express questions in Ivanov-Petrova geometry, Osserman geometry, and curvature homogeneity in ter…

This paper develops a new homology theory for biquandles and discusses geometric realizations.

In this paper, we prove a functorial aspect of the formal geometric quantization procedure of non-compact spin-c manifolds.

SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.

In this paper, we study how the notions of geometric formality according to Kotschick and other geometric formalities adapted to the Hermitian setting evolve under the action of the Chern-Ricci flow on class VII surfaces, including Hopf and Inoue surfaces, and on Kodaira surfaces.

Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from geometric data. As a by-product, it is shown that the evolution of the gradient of …

We study the geometry of complete generic Ricci solitons with the aid of some geometric-analytical tools extending techniques of the usual Riemannian setting.

We generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\mathbb{C}$) to geometrically infinite discrete isometry subgroups in the case of rank 1 symmetric spaces, and, under the assumption of bounded torsion, to the case of negatively pinched Hadamard manifolds. Eve…

In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\mathbb{C}$) to geometrically infinite discrete subgroups $Γ$ of isometries of negatively pinched Hadamard manifolds $X$. We then generalize a theorem of Bishop to prove that every discrete geome…

The study extends Dehn filling to Lie groups, ensuring geometric properties.

First constructed genus 2 Cantor set in 3D space.

We study the problem of rigidity of closures of totally geodesic plane immersions in geometrically finite manifolds containing rank $1$ cusps. We show that the key notion of K-thick recurrence of horocycles fails generically in this setting. This property was introduced in the recent work of McMullen, Mohammadi and Oh.…

We work in both the complex and in the para-complex categories and examine (para)-Kähler Weyl structures in both the geometric and in the algebraic settings. The higher dimensional setting is quite restrictive. We show that any (para)-Kaehler Weyl algebraic curvature tensor is in fact Riemannian in dimension at least 6…

Given a compact $n$-dimensional immersed Riemannian manifold $M^n$ in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then $M^n$ is homeomorphic to the sphere $S^n$. Also, we define a concept of finite geometrical type and prove that finite geometrical type h…

The paper geometrically characterizes graded manifolds and proves the Frobenius theorem.

Study geometric properties of surfaces with specific formulae.

The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.

The paper proves a geometric capacitary inequality for sub-static manifolds with harmonic potentials.

Introduces three types of partial bihamiltonian structures.

The volume of a credal set correlates with epistemic uncertainty in binary classification but not in multi-class.

Geometrical and appearance quality requirements set the limits of the current industrial performance in injection molding. To guarantee the product's quality, it is necessary to adjust the process settings in a closed loop. Those adjustments cannot rely on the final quality because a part takes days to be geometrically…

Develops theory of relatively geometric actions on CAT(0) cube complexes.

We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of…

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $μ$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p)$ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.

CantorNet tests geometric and topological complexity in neural networks.

We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian manifold. This requires extending the Tricerri-Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen …

Geometric theory explains substitutability in market outcomes based on production constraints.

PackIt creates a virtual space for testing geometric planning skills.