7543 papers
This paper establishes a sharp quantitative stability version of the Brascamp-Lieb inequality with a stability constant independent of the convex function, alongside uniform stability results for moment measures, by leveraging recent sharp stability versions of the Prékopa-Leindler inequality.
This paper generalizes scalar-valued holomorphic -contact and -symplectic structures to line bundle-valued analogues on compact complex manifolds, demonstrating that unlike their scalar counterparts, these new structures can admit projective examples, and investigates the positivity properties of their canonical bundles using recent regularisation results for -psh functions.
This paper establishes that the finite Osgood criterion on the drift term is both necessary and sufficient for finite-time blowup in the multiplicative stochastic heat equation on the interval , and extends this result to demonstrate instantaneous explosion on the real line by comparing solutions with those on the bounded domain.
This paper proposes a kinetic mathematical model for popularity-adaptive social networks that couples opinion dynamics with network evolution, introducing control laws to strategically influence connectivity and opinion spreading in order to mitigate polarization and foster consensus.
This paper establishes that the stability of -adjoint log canonical singularities on foliated surfaces undergoes sharp thresholds at and , which are proven to be optimal through a complete classification of these singularities for in terms of negative definite exceptional configurations.
This paper utilizes a computationally optimized variant of the Maximum Entropy Method to derive and prove two infinite families of non-Shannon entropy inequalities for five random variables, thereby advancing the understanding of the structure of the five-variable entropic region.
This paper presents methods to compute the number of -rational points with a specific -invariant on arbitrary modular curves, applying these techniques to classify the possible counts of cyclic -isogenies and points on Cartan modular curves for elliptic curves over number fields, while also providing an algorithm to determine the number of rational CM points.
This paper establishes a Faber-Krahn inequality for trees with a fixed matching number, a result that generalizes and implies the Klobůrštěl theorem regarding trees with specified numbers of interior and boundary vertices.
This paper presents the Reeb spaces of explicit real analytic functions that are not finite graphs, extending previous studies on smooth functions by incorporating topological considerations of level sets and real algebraic constructions.
This paper formulates and verifies a relative analogue of the Clemens conjecture for -log Calabi-Yau threefolds by establishing a perfect deformation/obstruction duality that suppresses virtual complications, thereby reducing relative Gromov-Witten invariants to classical enumerative counts of rational curves with balanced normal bundles.
This paper extends the theorem of the heart to generic small stable -categories by establishing sufficient conditions under which an exact functor induces isomorphisms of non-negative algebraic K-groups, thereby generalizing Quillen's dévissage theorem.
This paper proposes a new "minimum denoised subspace discrepancy decoder" for the blind identification of channel codes on binary symmetric channels, which combines Hamming and subspace metrics to provide rigorous theoretical guarantees and demonstrate superior performance over existing methods, particularly for random linear codes with limited data.
This paper characterizes Coxeter polytopes with finite volume in their Vinberg domains as quasiperfect polytopes of negative type and establishes that, for dimensions at least two, the Vinberg domain is the unique invariant properly convex domain if and only if the group action has finite covolume.
This paper extends the rigidity theory of quasihomomorphisms from discrete groups to real linear algebraic groups by proving that such maps can be constructed from homomorphisms and sections of bounded central extensions.
This paper challenges the prevailing view that tightening voltage angle bounds in the Direct-Current Optimal Transmission Switching problem requires solving an intractable longest path problem by presenting a novel polyhedral analysis that derives facet-defining inequalities to construct an extended formulation for the convex hull of the angle-based relaxation.
This paper proves that for the damped nonlinear Klein-Gordon equation in dimensions 2 to 5, any solution asymptotically approaching a superposition of four solitons with exactly one opposite sign evolves such that the three like-signed solitons arrange themselves into an equilateral triangle centered around the single oppositely signed soliton.
This paper establishes the global-in-time existence of solutions for the two-dimensional fully parabolic Keller–Segel system with critical mass for general initial data, removing previous requirements for radial symmetry or specific moment conditions by utilizing a reconstructed Lyapunov functional and refined regularity estimates.
This paper establishes closed-form expressions for the infinite series of arctanh(n⁻ᵏ) by linking them to gamma function infinite products, subsequently deriving new identities for the Riemann zeta function and Euler-Mascheroni constant, and analyzing the monotonicity, convexity, and asymptotic behavior of these sums.
This paper establishes the existence of nontrivial stationary periodic solutions to nonlinear Dirac equations on a three-dimensional torus with non-coercive potentials by employing a coercive perturbation to satisfy the Palais-Smale condition and deriving uniform estimates to pass to the limit.
This paper establishes uniform a priori estimates for solutions of semilinear planar Hamiltonian elliptic systems with Brezis-Merle critical nonlinearities using a novel blow-up approach combined with Liouville-type theorems, thereby resolving an open problem and proving the existence of positive solutions via Fixed Point Index theory.