arXiv research

Sharp spectral gap estimates on manifolds with integral curvature bounds.

Estimates the mass gap for domains with integral Ricci curvature bounds.

In this paper, we study the properties of the first global term in the polyhomogeneous expansions for Liouville's equation. We obtain rigidity and gap results for the boundary integral of the global coefficient. We prove that such a boundary integral is always nonpositive, and is zero if and only if the underlying doma…

Study bounds on self-shrinkers with bounded HA for applications.

The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.

Constructs coordinate systems from spectral curve sheaves.

Study on stable commutator length in RAAGs and Coxeter groups, proving spectral gaps and hardness results.

The paper proves various inequalities on gradient shrinking Ricci solitons.

Global stability proved for Navier-Stokes equations on hyperbolic space.

Study gap phenomenon in flat manifolds with Ricci curvature.

Confirms unique eigenfunction in hyperbolic packing has maximal spectral gap.

The paper connects Schrödinger equations to geodesics on a 2-surface.

It is well known that certain combinations of configuration space integrals defined by Bott and Taubes produce cohomology classes of spaces of knots. The literature surrounding this important fact, however, is somewhat incomplete and lacking in detail. The aim of this paper is to fill in the gaps as well as summarize t…

Paper proves Simon's third gap conjecture for minimal surfaces in spheres.

The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.

Paper integrates ML with physics models for engineering and environmental challenges.

Let $M$ be a connected, noncompact, complete Riemannian manifold, consider the operator $L=\DD +\nn V$ for some $V\in C^2(M)$ with $\exp[V]$ integrable w.r.t. the Riemannian volume element. This paper studies the existence of the spectral gap of $L$. As a consequence of the main result, let $\rr$ be the distance functi…

New theorem shows curvature concentration depends linearly on volume ratio.

We study integral and pointwise bounds on the curvature of gradient shrinking Ricci solitons. As applications we discuss gap and compactness results for gradient shrinkers.

In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result c…

The $L^2$-$\partial\overline\partial$-Lemma is extended to complete Kähler manifolds with a gap in the spectrum.

Factorial moments are convenient tools in particle physics to characterize the multiplicity distributions when phase-space resolution ($Δ$) becomes small. They include all correlations within the system of particles and represent integral characteristics of any correlation between these particles. In this letter, we sh…

New Holder bounds improve variational inference by flattening thermodynamic curves.

Study on Ricci flow on 4-spheres, proving standard sphere convergence.

In 1965 Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in $R^3$ is at least $2π^2$ and attains this minimal value if and only if the torus is a Möbius transform of the Clifford torus. This was recently proved by Marques and Neves. In this paper, we show for tori there is …

Data visualization and interaction with large data sets is known to be essential and critical in many businesses today, and the same applies to research and teaching, in this case, when exploring large and complex mathematical objects. GAP is a computer algebra system for computational discrete algebra with an emphasis…

Improved approximation for socially fair clustering with $\ell_p$-objective.

We construct some explicit quasihomogeneous algebraic solutions to the associativity (WDVV) equations by using analytical methods of the finite gap integration theory. These solutions are expanded in the uniform way to non-semisimple Frobenius manifolds.

GACELA fills long gaps in musical audio with a GAN and context conditioning.

Researchers find spectral gaps in quantum flag manifolds using twisted operators.

LLapDiff models irregular multivariate time series without step-by-step integration.

Study identifies a Strategic Gap in market efficiency due to AI-driven timing and complexity in disclosure.

Given a constant magnetic field on Euclidean space ${\mathbb R}^p$ determined by a skew-symmetric $(p\times p)$ matrix $Θ$, and a ${\mathbb Z}^p$-invariant probability measure $μ$ on the disorder set $Σ$ which is by hypothesis a Cantor set, where the action is assumed to be minimal, the corresponding Integrated Density…

We present the Integrated Size and Price Optimization Problem (ISPO) for a fashion discounter with many branches. Based on a two-stage stochastic programming model with recourse, we develop an exact algorithm and a production-compliant heuristic that produces small optimality gaps. In a field study we show that a distr…

We prove a quantitative bi-Lipschitz nonembedding theorem for the Heisenberg group with its Carnot-Carathéodory metric and apply it to give a lower bound on the integrality gap of the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem.

KZImputer improves time series data quality with adaptive imputation for short to medium-sized gaps.

Paper generalizes Bakry-Émery calculus for curvature and applies to Markov chains.

Paper withdrawn because of a gap in the proof of Proposition 3 of Thomas Schick: "Integrality of L2-Betti numbers", Math. Ann. 317, 727-750 (arXiv.org/abs/math.gt/0001101). Most results of the withdrawn paper were based on this proposition.

Paper studies a new curvature system and proves rigidity and gap theorems.

Predicting the outcomes of integrating Unmanned Aerial Systems (UAS) into the National Aerospace (NAS) is a complex problem which is required to be addressed by simulation studies before allowing the routine access of UAS into the NAS. This thesis focuses on providing 2D and 3D simulation frameworks using a game theore…

The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modellin…

Special class of surfaces in five-dimensional sphere in $C^3$ is considered. Immersion equations for minimal tori of that class are shown to be reducible to the equation $u_{z\bar z}=e^u-e^{-2u}$ which is integrable by means of inverse scattering method. Finite-gap minimal tori are constructed.

In this paper we show that all totally real superconformal minimal tori in $CP^2$ correspond with doubly-periodic finite gap solutions of the Tzitzeica equation $ω_{z{\overline z}}=e^{-2ω}-e^ω$ Using the results on the Tzitzeica equation in integrable system theory, we describe explicitly all these tori by Prym-theta…

A generic surface in Euclidean 3-space is determined uniquely by its metric and curvature. Classification of all special surfaces where this is not the case, i.e. of surfaces possessing isometries which preserve the mean curvature, is known as the Bonnet problem. Regarding the Bonnet problem, we show how analytic metho…

We derive point-wise and integral rigidity/gap results for a closed manifold with harmonic Weyl curvature in any dimension. In particular, there is a generalization of Tachibana's theorem for non-negative curvature operator. The key ingredients are new Bochner-Weitzenböck-Lichnerowicz type formulas for the Weyl tensor,…

Calibrations help estimate volumes on odd spheres without gaps.

The paper solves integrable systems of PDEs, including famous equations.

Bayesian quadrature uses probabilistic models for estimating intractable integrals.