arXiv research

New inequalities for convex curves with multiple geometric factors.

Generalizes sigma model with Lie algebroid structure and geometric conditions.

Paper finds conditions for special geometric structures on certain spaces.

Maps between non-compact surfaces can have geometric kernels under certain conditions.

Geometric invariant theory introduces stability conditions mirroring abelian category theory.

Geometric approach finds correspondences between different conditions.

Derives energy-momentum tensor from Standard Model, examines energy conditions.

Let $X_{0}$ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric …

Proof of local well-posedness for a specific boundary condition in general relativity.

The aim of this paper is to establish two fundamental measure-metric properties of particular random geometric graphs. We consider $\varepsilon$-neighborhood graphs whose vertices are drawn independently and identically distributed from a common distribution defined on a regular submanifold of $\mathbb{R}^K$. We show t…

Study on slow convergence in geometric variational problems.

A homotopy equivalence between a hyperbolic 3-manifold and a closed irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic manifold satisfies a purely geometric condition. There are no known examples of hyperbolic 3-manifolds which do not satisfy this condition.

The paper finds sign-changing solutions for a specific type of elliptic equation.

We prove that the introduction of the class of geometrically atomic bundle maps by Harvey and Lawson in their theory of singular connections is not necessary because an arbitrary map satisfies the conditions of geometric atomicity.

Solves initial boundary value problem for vacuum Einstein equations and proves geometric uniqueness.

In this note, we extend our previous work on the inverse $σ_k$ problem. Inverse $σ_{k}$ problem is a fully nonlinear geometric PDE on compact Kähler manifolds. Given a proper geometric condition, we prove that a large family of nonlinear geometric flows converges to the desired solution of the given PDE.

Study geometric properties of SGL submanifolds in a specific manifold.

Generalizes Cheeger inequality to Carnot-Carathéodory spaces.

New theory for local parameterization of deep ReLU networks.

Quasispheres can be approximated by smooth spheres.

We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle. --Parameterize arbitrage strategies by its holonomy. --Give the Fundamental Theorem of Asset …

The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the corresponding principal circle bundle and we extend the notion of a polarization.

We obtain a Bonnet-Myers theorem under a spectral condition: a closed Riemannian manifold $(M^n,g)$ for which the lowest eigenvalue of the Ricci tensor $ρ$ is such that the Schrödinger operator $(n-2)Δ+ ρ$ is positive has finite fundamental group. As a continuation of our earlier results, we obtain isoperimetric inequa…

Geometric study of cuspidal $S_1$ singularities using diffeomorphisms and isometries.

The study examines extensions of Lie algebras with specific geometric structures.

We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both position-independent and position-dependent integration times. In the former case we find that the conditions for geometric ergodicit…

The paper explores geometric finiteness in mapping class groups and constructs new examples of these subgroups.

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\sqrtκ)$ and thus achieves the optimal …

Sharp pinching conditions restrict the geometry and topology of submanifolds.

Study of geometric structures on manifolds, focusing on integrability conditions.

We prove a Lorentzian splitting theorem with weakened curvature conditions.

New geometric quantities help classify manifolds and relate to entropy.

Geometric approach to moment maps in complex geometry.

New curvature condition helps organize high-curvature regions in geometric flows.

New geometric properties discovered in a specific Frobenius manifold.

Paper shows geometric frequency and Lagrange derivative equivalence for electric and fluid systems.

Solves geometric problems using fully nonlinear equations and Morse theory.

SGD and stochastic gradient descent converge at optimal rates for certain non-convex functions.

New method detects dangerous states in gridworlds using geometric defects.

Study shows observability for Schrödinger equations on product manifolds with specific conditions.

Geometric deformations preserve post-Lie algebra structure in regularity structures.

Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly disconnected). We characterise the subsurfaces which lead to virtually abelian ge…

Uniformly perfect Morse boundaries characterize geometric properties of groups.

Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction to the slow flow. The focus of this work is on a proposition and discussion of a …

Study of geometric structures on projective space complement without Schwarz conditions.

New method uses geometric mean to avoid non-collapsibility in case-control studies.

A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtained

The study classifies steady Ricci solitons based on geometric conditions.