2345 papers
This paper characterizes the Legendre, Laplace, and identity transforms as the unique continuous, contravariant valuations with specific conjugation or duality properties on spaces of convex and log-concave functions.
This paper focuses on convex polygons in the plane by summarizing and comparing Gibbs coordinates (based on entropy maximization and exponential functions) with Wachspress coordinates (rational functions), identifying their points of agreement and divergence, and demonstrating how Gibbs coordinates for polygons with rational vertices can be interpreted as algebraic functions.
This paper establishes that the rook polynomial of grid polyominoes coincides with the h-polynomial of their corresponding coordinate rings by utilizing simplicial complex theory to generalize previous findings on frame polyominoes.
This paper introduces and proves the convergence of a Martingale Sinkhorn algorithm in arbitrary dimensions for solving the martingale Benamou–Brenier optimal transport problem, extending the theory to marginals with finite moments of order without requiring compact support.
This paper classifies all pairs consisting of a -bundle over a non-rational ruled surface and its relatively maximal connected automorphism group over an algebraically closed field of characteristic zero.
This paper proposes a robust, contour integral-based algorithm tailored for the Jordan-Wielandt matrix pencil to efficiently compute a few generalized singular values with rapid convergence and high accuracy, overcoming the limitations of directly applying the standard FEAST algorithm.
This paper establishes that convex-cocompact representations of finitely generated groups into the isometry group of infinite-dimensional hyperbolic space form an open set, enabling the construction of new surface group representations via bending that are distinct from those classified by Monod and Py.
This paper proves a conjecture by Raskind, Spiess, Colliot-Thélène, and Sansuc regarding the structure of the Chow group of zero-cycles on geometrically Kummer surfaces over -adic fields and provides the first unconditional evidence for a local-to-global principle for zero-cycles on such surfaces by demonstrating that the Brauer-Manin obstruction is the sole obstruction to weak approximation in specific cases.
This paper demonstrates that the occupation measure of planar Brownian motion exhibits a constant height gap of $5/\pi$ across its outer boundary, a result derived by leveraging the expected area of the domain delimited by a Brownian bridge and drawing parallels to height gap properties in the Gaussian free field and Brownian loop soup.
This paper characterizes graphs whose edge ideals possess Scarf resolutions as exactly the gap-free forests, while also classifying connected graphs where all powers of their edge ideals admit Scarf resolutions and providing recursive constructions for these complexes.
This paper develops an asymptotic expansion formula for bootstrap coverage probabilities in high dimensions to theoretically explain why third-moment matching wild bootstrap methods outperform normal approximations, demonstrating that such methods achieve second-order accuracy without studentization under specific covariance structures or via a double wild bootstrap approach.
This paper demonstrates that the classical Mazzeo-Pacard gluing method can be successfully extended to construct singular solutions for the fully non-linear -Yamabe equation in dimensions , provided the singular set consists of disjoint closed submanifolds with dimensions strictly less than .
This paper compiles a collection of polynomial Diophantine equations that are deceptively simple to formulate yet remain notoriously difficult to solve, highlighting significant open problems in the field.
This paper investigates heat equations with non-local Robin boundary conditions on bounded Lipschitz domains, demonstrating that while certain boundary operators can destroy the positivity-preserving property of the solution semigroup, the system still achieves ultracontractivity and exhibits eventual positivity under mild assumptions.
This paper establishes new mean curvature rigidity theorems for spin fill-ins with non-negative scalar curvature by employing two distinct spinorial techniques—an APS boundary value problem extension and an index-theoretic comparison—to resolve questions posed by Miao and Gromov, while also deriving a novel Witten-type mass inequality for asymptotically Schwarzschild manifolds.
This paper proposes and validates a robust nonlinear multilevel solution strategy for the Diffusive Wave equation on highly perforated urban domains by integrating a specialized multiscale coarse space with Schwarz-based nonlinear preconditioning methods to ensure scalability and efficiency.
This paper establishes an almost equivalence between the equivariant Tamarkin category and the category of derived complete modules over the Novikov ring, thereby clarifying the relationship between Tamarkin's extra variable and Novikov rings.
This paper establishes a correspondence between model structures and a single hereditary complete cotorsion pair on weakly idempotent complete extriangulated categories, thereby generalizing previous results by Beligiannis-Reiten and Cui et al., and provides methods to construct such model structures from silting objects and co--structures.
This paper confirms Oort's conjecture by proving that for even and , every geometric generic member of the maximal supersingular Ekedahl-Oort stratum in the moduli space of principally polarized abelian varieties has an automorphism group consisting only of , while also establishing the result for the specific case of for any prime .
This paper establishes the distributional stability of sparse inverse covariance matrix estimators by deriving explicit local Lipschitz bounds on the Kantorovich distance between their distributions under true and contaminated data scenarios, while also extending these results to standard covariance and eigenvalue estimators.