6238 papers
Motivated by non-abelian Hodge theory, this paper formulates a Hodge-theoretic version of Grothendieck's anabelian conjecture by replacing Galois actions with natural -actions, proving an analog of Mochizuki's theorem for smooth projective hyperbolic curves over and extending the result to higher-dimensional ball quotient manifolds.
This paper investigates the structural implications of vanishing -degree Turán densities in hypergraphs, proving that for -uniform hypergraphs with vanishing 2-degree Turán density, a specific global vertex ordering (2-vanishing order) must exist, thereby generalizing classical results on zero Turán density and demonstrating that unlike the classical case, 2-degree Turán densities accumulate at zero.
This paper establishes that Sobolev maps on the product of two Euclidean domains with invertible differentials preserving or swapping the factor spaces are necessarily split when the dimension , a result that fails for and for lower regularity spaces with .
This paper revises Gauss's Lemma by introducing the concept of "metrical distortion" as a non-identity isometry between double tangential and tangential spaces, and concretely defines the exterior differential via covariant gradient transport to incorporate a "differential slip" representing scalar gauge theory, ultimately distinguishing between geodesically radial volume preservation (metrical distortion) and length preservation (exponential mapping) through the example of the 2-sphere.
This paper establishes the existence of regular global and exponential attractors with finite fractal dimension for the planar Coleman--Gurtin heat equation with memory and rough anisotropic diffusion encoded by a Beltrami coefficient, utilizing a combination of instantaneous smoothing techniques, maximal parabolic regularity, and quasiconformal estimates.
This paper investigates the behavior of Galois periods under the local theta correspondence for even orthogonal and symplectic groups by comparing their multiplicities, constructing explicit transfer maps, and establishing both adjoint and relative character relations.
This paper establishes the almost sure Hausdorff dimension of the images and graphs of a broad class of random complex series, which encompasses famous deterministic functions like the Weierstrass and Riemann functions, thereby providing a probabilistic framework to predict the exact dimension values of their deterministic counterparts.
This paper introduces two numerical frameworks—a strong-competition penalty method with damped Gauss-Seidel iterations and a projected gradient method with an accelerated variant—to solve elliptic systems governed by nonconvex partial segregation constraints where three nonnegative components must have a vanishing pointwise product.
This paper advances the study of outer length billiards by proving 3- and 4-periodic versions of the Ivrii conjecture and demonstrating the existence of functional spaces of billiard tables with invariant curves of -periodic points, including an explicit geometric parameterization for the centrally symmetric case.
This paper proposes a Newton-based algorithm with an Armijo-like line search strategy to solve multiobjective interval optimization problems by establishing a link between weakly Pareto optimal and Pareto critical points, proving its convergence, and validating its effectiveness through numerical experiments and a portfolio optimization application.
This paper establishes a sharp topological dichotomy for slices of the Sierpinski tetrahedron, demonstrating that slices at dyadic rational heights possess finitely many connected components with infinite first Čech homology, whereas slices at non-dyadic rational heights are totally disconnected with vanishing positive-degree homology.
This paper determines all -biderivations for the Witt algebra, the Virasoro algebra, the -algebras , and their universal central extensions , and subsequently presents applications of these results.
This paper constructs a new class of simple weight modules for the twisted Heisenberg-Virasoro algebra and gap- Virasoro algebras by utilizing restricted modules over their positive part subalgebras, yielding novel results particularly for the mirror Heisenberg-Virasoro algebra when .
This paper characterizes the spectrum of values for weak uniform Diophantine exponents associated with lattices in arbitrary dimensions.
This paper establishes the existence and uniqueness of a non-negative, piecewise smooth, and symmetric potential in that maximizes the sum of the first two Dirichlet eigenvalues for Sturm-Liouville operators, demonstrating that its nonzero part is determined by the solution to the pendulum equation via measure differential equations and weak convergence.
This paper proposes a physically consistent signal model and an alternating optimization framework for downlink sum-rate maximization in STAR beyond-diagonal RISs with per-element amplification, achieving substantial performance gains over conventional passive systems while ensuring hardware feasibility and passivity.
This paper establishes the first large deviation principle for convolutional neural networks in the infinite-channel regime, characterizing the asymptotic behavior of conditional covariance matrices and posterior distributions under Gaussian priors while also providing streamlined proofs for their Gaussian equivalence and concentration.
This paper constructs an arbitrary-order asymptotic expansion for the quantum evolution of coherent states in self-interacting bosonic field theories, refining previous leading-order results by applying Hepp's method to both spatially cutoff models and non-polynomial analytic interactions.
This paper establishes a unified framework using symplectic field theory functorial properties to generate finite algebraic (planar) torsions, thereby confirming a conjecture by Latschev and Wendl regarding stably fillable examples in dimensions five and higher and demonstrating the ubiquity of tight, non-weakly fillable contact structures on spheres in those dimensions.
This paper proves Oort's conjecture that the automorphism group of a generic principally polarized supersingular abelian variety in characteristic is , except for the specific cases of genus 2 or 3 with , while also providing an explicit description of the -locus in the corresponding Rapoport-Zink space and establishing analogous results for supersingular -divisible groups.