A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The absolute Galois group of 3-manifolds determines their structure up to homeomorphism.
Determine lens spaces as closures of homology cobordisms over planar surfaces.
We prove that every lens space contains a genus one homologically fibered knot, which is contrast to the fact that some lens spaces contain no genus one fibered knot. In the proof, the Chebotarev density theorem and binary quadratic forms in number theory play a key role. We also discuss the Alexander polynomial of hom…
Modular knots follow Chebotarev law from surgeries on hyperbolic fibered links.
Extends Floquet-Bloch theory to nilpotent groups for geometric applications.
We discuss the relationship between two analogues in a 3-manifold of the set of prime ideals in a number field. We prove that if is a sequence of knots obeying the Chebotarev law in the sense of Mazur and McMullen, then is a stably generic link in the sense of Mih…
Proves density and mass theorems for specific initial data sets.
New integral theorems improve density function estimations.
It is showed that on a plane with a radial density the Four Vertex Theorem holds for the class of all simple closed curves if and only if the density is constant. But for the class of simple closed curves that are invariant under a rotation about the origin, the Four Vertex Theorem holds for every radial density.
The paper proves density and positive mass theorems for incomplete manifolds.
Characterizes density-valued symplectic forms on multisymplectic manifolds.
The paper introduces new estimators for multivariate functions using Fourier methods.
Polynomial density theorem for specific subgroup orbits in quotient spaces.
Proves positive mass theorem for non-spin weighted manifolds.
This paper studies neural network operators and their convergence properties.
Paper resolves Huisken's conjecture without strict genus drop theorem.
We suggest an algorithm allowing to obtain some new integral-geometric formulae from the existing formulae of Crofton type. These new formulae are applied to get smooth versions of BKK theorem. The algorithm is based on the calculations in the ring of normal densities on a manifold.
Paper proves minimal resistance for a body in a fluid with decreasing density.
The paper computes a residue density for a specific Laplacian on compact manifolds.
Survey on smooth function and form density in Riemannian Sobolev spaces.
Motivated by analogies with basic density theorems in analytic number theory, we introduce a notion (and variations) of the homological density of one space in another. We use Weil's number field/ function field analogy to predict coincidences for limiting homological densities of various sequences $\mathcal{Z}^{(d_1,\…
Proves a limit on hyperplanes in complex manifolds.
Quantum assets are priced using a new theorem, extending classical asset pricing.
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion free connection introduced recently by the last two authors. We develop two new tools for studying weighted sectional curvature bounds: a new weighted Rauch comparison theorem and a modifie…
We prove that a minimal disc in a CAT(0) space is a local embedding away from a finite set of "branch points". On the way we establish several basic properties of minimal surfaces: monotonicity of area densities, density bounds, limit theorems and the existence of tangent maps. As an application, we prove Fary-Milnor's…
Extends a Liouville theorem for stable minimal hypersurfaces.
The paper explores density of stable mappings and their properties.
The index theorem connects anomalies on a domain wall to global integrals.
We provide very general symmetrization theorems in arbitrary dimension and codimension, in products, warped products, and certain fiber bundles such as lens spaces, including Steiner, Schwarz, and spherical symmetrization and admitting density.
New findings on PAC learning and marginal distribution estimation.
The study proves that certain stable minimal hypersurfaces must be cylindrical.
In this paper we introduce two new notions of sectional curvature for Riemannian manifolds with density. Under both notions of curvature we classify the constant curvature manifolds. We also prove generalizations of the theorems of Cartan-Hadamard, Synge, and Bonnet-Myers as well as a generalization of the (non-smooth)…
In this paper we have proved several approximation theorems for the family of minimal surfaces in R^3 that imply, among other things, that complete minimal surfaces are dense in the space of all minimal surfaces endowed with the topology of C^k convergence on compact sets, for any k. As a consequence of the above densi…
New examples of embeddings defy Anosov representation limits.
Paper proves integrability and entropy compactness for Kähler potentials with uniform log-log threshold.
New examples show embeddings not approximated by Anosov representations.
We study generalizations of Reifenberg's Theorem for measures in under assumptions on the Jones' -numbers, which appropriately measure how close the support is to being contained in a subspace. Our main results, which holds for general measures without density assumptions, give effective measure bounds…
In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifold with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.
Kernel Density Machines learn probability densities without structural assumptions.
A new kernel framework analyzes spatio-temporal data from dynamic equations.
Paper proves linear convergence of SCMS algorithm for directional data.
In this paper we extend Thurston's hyperbolic Dehn surgery theorem to a class of geometrically infinite hyperbolic 3-manifolds. As an application we prove a modest density theorem for Kleinian groups. We also discuss hyperbolic Dehn surgery on geometrically finite hypebolic cone-manifolds.
It was pointed out to us that the proof of a crucial lemma (Lemma 5.3) in the paper is incorrect. Thus the approximation theorem (Theorem 0.1) for L^2 torsion of an amenable covering of a finite simplicial complex remains unproved. However, results and proofs of the first four sections (in particular, the approximation…
In 1992, Reid asked whether hyperbolic 3-manifolds with the same geodesic length spectra are necessarily commensurable. While this is known to be true for arithmetic hyperbolic 3-manifolds, the non-arithmetic case is still open. Building towards a negative answer to this question, Futer and Millichap recently construct…
We prove that a theorem of Pawlucki, showing that Whitney regularity for a subanalytic set with a smooth singular locus of codimension one implies the set is a finite union of differentiable manifolds with boundary, applies to definable sets in polynomially bounded o-minimal structures. We give a refined version of Paw…
The paper studies knot densities under various constraints and degenerations.
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical -estimation. We interpret the KDE based on a radial, positive semi-definite ke…
We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price interval invariant, we prove a…