7189 papers
The paper proves that every locally flat topological embedding of a 3-manifold into a smooth 5-manifold can be approximated by a smooth embedding via a small homotopy, thereby establishing that topologically locally flat concordance implies smooth concordance for surfaces in 4-manifolds.
This paper establishes the well-posedness and maximal regularity of weak solutions to parabolic Cauchy problems with bounded, time-independent, uniformly elliptic coefficients in weighted tent spaces by extending singular integral operator theory via off-diagonal estimates and employing interior representation techniques to prove uniqueness.
This paper describes the moduli space of semi-homogeneous vector bundles on an abelian variety with totally degenerate reduction via non-Archimedean uniformization, identifying its essential skeleton with a tropical analogue and constructing a surjective analytic morphism from the character variety of the analytic fundamental group to the moduli space of semistable vector bundles with vanishing Chern classes.
The paper establishes a monotonicity property for the volumes of central hyperplane sections of 1-symmetric convex bodies and a corresponding convexity property for Rademacher sums regarding projections, with applications to chessboard cutting.
This paper constructs non-affine -valued maps on -dimensional tori (for ) that are not homotopic to affine maps, a result that contrasts sharply with the single-valued case and is achieved by establishing necessary and sufficient algebraic conditions on induced morphisms.
This paper establishes theoretical uniform-in-time error bounds for the deterministic ensemble transform Kalman filter applied to infinite-dimensional nonlinear dynamical systems, demonstrating that appropriate multiplicative covariance inflation ensures bounded estimation errors and justifying its practical effectiveness.
This paper establishes central and non-central limit theorems for functionals of stationary Gaussian fields integrated over growing product domains, analyzing both separable covariance structures with quantitative bounds for Hermite polynomials and extensions to Gneiting-class or additively separable covariances.
This paper establishes that the inverse mean curvature flow by parallel hypersurfaces in space forms exists if and only if the initial hypersurface is isoparametric, providing explicit solutions and characterizing their long-term behavior and collapsing limits based on the number and multiplicity of principal curvatures.
This paper establishes an ergodic theorem for Markov chains indexed by trees of arbitrary shape under specific geometric and regularity conditions, while also demonstrating that for stationary and reversible chains, the linear tree structure minimizes the variance of empirical average estimators.
This paper presents an algorithmic procedure combining Padé approximants and Borel-Écalle summation to construct rational approximations of functions with essential singularities, specifically applying the method to generate highly accurate tritronquée solutions and pole distributions for Painlevé's first equation.
This paper refines classical embedding theorems by proving that recursively presented groups admit quasi-isometric malnormal embeddings into finitely presented groups with the congruence extension property and controlled decidability, while also establishing that any countable group can be malnormally embedded into a finitely presented group with a prescribed word length function.
This paper investigates the division properties of commuting polynomials with rational and integer coefficients, revealing algebraic particularities related to weighted sums on cycle graphs with pendant edges and exploring commuting polynomials over fields of positive characteristic.
This paper introduces an axiomatic framework for allocation mechanisms in decentralized exchange markets that account for frictional transfer costs, characterizing robust linear mechanisms and "Robust Conditional Mean" mechanisms while linking them to literature on decentralized risk sharing.
This paper establishes an averaging formula to compute the Nielsen number of any -valued affine map on an infra-nilmanifold, extending previous results known for single-valued maps and -valued maps on nilmanifolds.
This paper determines the percolation and connectivity thresholds for random subgraphs of the permutahedron, a highly-symmetric polytope that generalizes the Erdős-Rényi random graph and the percolated hypercube, while introducing a novel graph exploration technique and initiating the study of the permutahedron's isoperimetric properties.
This paper establishes a purity theorem for -adic local systems on rigid-analytic varieties with semistable formal models by proving that such systems are semistable if and only if their restrictions to the irreducible components of the special fiber are semistable, utilizing analytic prismatic -crystals and a newly derived prismatic purity theorem.
This paper extends Bobkov and Chistyakov's upper bounds on concentration functions to a multivariate entropic setting using pointwise density estimates, thereby deriving sharp bounds on the volumes of noncentral sections of isotropic convex bodies.
This paper establishes a comprehensive well-posedness theory for parabolic Cauchy problems with time-independent, uniformly elliptic, bounded measurable complex coefficients, demonstrating that tempered distributions in homogeneous Hardy–Sobolev or Besov spaces serve as valid initial data for weak solutions with gradients in weighted tent spaces when source terms are of Lions' type.
This paper presents a scalable monolithic Newton-Krylov-multigrid solver that extends efficient spatial multigrid methods to a space-time waveform relaxation framework for the all-at-once solution of discretized Navier-Stokes equations.
This paper classifies deformation quantizations of smooth, admissible symplectic supervarieties by generalizing the Bezrukavnikov-Kaledin result to the super case, establishing a correspondence with their even reduced symplectic varieties, and applying these findings to nilpotent orbits of basic Lie superalgebras.