55 papers
This paper establishes quantitative bounds on the size of dense subsets of hypercubes that can be embedded into other metric spaces with specific distortion constraints, while also deriving geometric applications regarding nonpositive Alexandrov curvature targets and improving bounds for embeddings of paths and trees.
This paper establishes the local stability of the Betke-Henk-Wills conjecture under metric perturbations by deriving explicit, geometry-invariant bounds on the rotation radius that preserve the lattice point enumerator for integer boxes and identifying a sharp threshold for the invariance of integer hulls in -balls.
This paper introduces a novel approach using disintegration maps to establish criteria for identifying metric measure foliations based on the geometric arrangement of conditional measure supports in Wasserstein space, while also demonstrating the framework's application to studying perturbations of such foliations.
This paper compares various recently proposed notions of non-rigidity for horizontal vectors in Carnot groups, which are motivated by the study of monotone sets and Whitney extension properties.
This paper demonstrates that a 1958 argument by Rogers provides a proof for Vaaler's 1979 theorem regarding sections of the cube and facilitates certain generalizations of the result.
This paper establishes that magnitude is continuous on the open and dense subset of skew finite subsets within the space of finite subsets of by deriving explicit weight measure formulas for their cubical thickenings and proving the convergence of their magnitudes.
This paper investigates the multifractal properties of the exceptional set in the Lüroth expansion where the maximal run-length function exhibits linear growth, specifically establishing the Hausdorff dimension for sets defined by prescribed lower and upper limits of the ratio between the run-length and the number of digits.
This paper demonstrates that while a continuous map into a metric space is of bounded variation if and only if its composition with every Lipschitz function is of bounded variation, this characterization fails for discontinuous maps in spaces like , infinite metric trees, and Laakso-type spaces, though it remains valid for ultrametric spaces without continuity assumptions.
This paper establishes the compactness of a character variety classifying continuous group actions on algebraic real hyperbolic spaces of arbitrary dimension, unifying previous compactifications and proving rigidity results for irreducible representations via the introduction of algebraic and abstract cross-ratios.
This paper establishes a universality principle for visibility in hyperbolic space, proving that the critical intensity and mean visible volume for a Poisson process of -geodesic hyperplanes are independent of the interpolation parameter and identical to the case of totally geodesic hyperplanes.
This paper extends the classical sharp upper bound on central hyperplane sections of a regular simplex to a probabilistic framework involving negative moments of centered log-concave random variables, revealing a phase transition in the extremizing distributions for new sharp reverse Hölder-type inequalities.
This paper establishes a dimension-free Gehring-Hayman inequality for quasigeodesics in infinite-dimensional spaces by developing a new approach that relaxes previous constraints on geodesics and quasiconformal equivalence, thereby affirmatively resolving a long-standing open problem regarding the relationship between uniformity and Gromov hyperbolicity in Banach spaces.
This paper presents new geometrically distinct five-dimensional sphere packings and a nine-dimensional kissing configuration that match existing optimal records without surpassing them, thereby expanding the known constructions of conjecturally optimal arrangements.
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.
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.