2549 papers
This paper establishes nontangential maximal function estimates for the gradient of solutions to elliptic operators with variable, bounded, measurable coefficients on Lipschitz domains, addressing a mixed boundary value problem with Neumann and Dirichlet-regularity data that generalizes both pure boundary problems and the classical Laplacian case.
This paper establishes sharp rates of propagation of chaos for McKean-Vlasov equations with non-linear measure-dependent coefficients, applying these results to derive uniform-in-time convergence guarantees for mean field Langevin dynamics, control, and games by combining the BBGKY hierarchy with weak propagation techniques.
This study mathematically analyzes a chemostat model of obligate mutualism to demonstrate that incorporating mortality significantly enriches the system's dynamical repertoire, enabling complex phenomena such as multistability, oscillatory coexistence, and diverse bifurcations that are absent in mortality-free scenarios.
This paper investigates -categories by comparing the -categories obtained via core and localization functors in the limit , demonstrating that the latter is a reflective localization of the former while also exploring intermediate localizations arising from coinductive notions of invertibility.
This paper introduces the Block Sparse Tensor Train (BSTT) sketch, a structured random projection that unifies existing TT-adapted sketching operators and achieves linear scaling in tensor order and subspace dimension, thereby enabling quasi-optimal error bounds for tensor factorization and rounding tasks.
This paper establishes that for generic smooth compact initial surfaces, the mean curvature flow in develops only isolated spherical or nondegenerate neck pinch singularities at the first singular time.
This essay introduces conformal symmetry by examining the Yamabe operator and its applications in conformal differential geometry and representation theory.
This paper establishes the equivalence of three notions of rank for matrices of multilinear forms, thereby generalizing Flanders' classical result, correcting prior work by Fortin and Reutenauer, resolving a question posed by Lampert, and proving a special case of the conjecture linking analytic and partition ranks of tensors.
This paper proves an asymptotically optimal bound for the concentration function of a sum of independent integer random variables, confirming that the sum's maximum point probability is bounded by that of a corresponding sum of minimal-variance variables when the total variance is sufficiently large, thereby extending the result to separable Hilbert spaces.
This paper investigates the asymptotic convergence of partial sums and remainders of the Dirichlet eta function to establish that the continuity of a specific limit ratio within the left half of the critical strip is equivalent to the truth of the Riemann Hypothesis, while also offering insights into the Simple Zeros Conjecture.
This paper introduces and analyzes the convergence of a proximal-type algorithm with line search and inertial methods for solving DC programs under the Kurdyka-Łojasiewicz property, demonstrating its effectiveness in variable selection for linear regression.
This paper investigates the distribution of zeros for a specific class of polynomials and their derivatives, ultimately proving a weak variant of Sendov's conjecture for polynomials whose zeros are real and share the same sign.
This paper investigates triangular line arrangements on the projective plane by proving their combinatorics are always realized by Roots-of-Unity-Arrangements, establishing conditions for their freeness, and demonstrating that freeness is not determined solely by weak combinatorics.
This paper investigates the local cyclicity and the growth of rational point groups for isogeny classes of abelian varieties over finite fields characterized by Weil polynomials of the form , utilizing a specific criterion involving the coprimality of the polynomial's derivative and radical at .
This paper establishes that a quasi-compact Kähler manifold admitting a complex polarized variation of Hodge structures with zero-dimensional fibers is algebraically hyperbolic and satisfies the generalized big Picard theorem, while also demonstrating that a finite étale cover of such a manifold admits a compactification where the boundary complement is Picard hyperbolic and all non-boundary subvarieties are of general type.
This paper establishes that a compact Kähler manifold whose dual Kähler cone contains a rational interior point has a projective Albanese variety, thereby resolving the Oguiso–Peternell problem for Ricci-flat manifolds and addressing related algebraicity questions for threefolds.
This paper constructs group-theoretic analogues of Johnson/Morita cocycles for pro-l groups to define Galois-cohomological classes for smooth curves, which are then used to demonstrate the existence of a non-hyperelliptic curve whose Ceresa class has a torsion image under the l-adic Abel-Jacobi map.
This paper proves that the natural density of the sequence of Ulam numbers is zero, meaning the proportion of Ulam numbers within the interval approaches zero as tends to infinity.
This paper establishes a combinatorial framework for K-stability of polarized spherical varieties, providing an explicitly checkable sufficient condition for the existence of constant scalar curvature Kähler metrics and demonstrating the equivalence between G-uniform K-stability and K-polystability for specific families near the anticanonical bundle.
This paper establishes the pseudo-effectivity of the relative canonical divisor for morphisms with non-uniruled generic fibers in positive characteristic by proving that sufficiently ample cyclic covers of non-uniruled bases remain non-uniruled, a result derived from a new cohomological criterion for uniruledness.