66 papers
This paper establishes a necessary and sufficient condition for the convergence of infinite products of rational inner functions on the polydisk and extends the concepts of Malmquist-Takenaka bases and unwinding to higher dimensions.
This paper establishes a logarithmic Bott localization formula for global holomorphic sections of on a compact complex manifold with a simple normal crossings divisor, extending the theory to non-isolated zero schemes that are local complete intersections and providing a current-theoretic formulation that identifies the local residue with a Coleff-Herrera current.
This paper addresses an Erdős-Herzog-Piranian problem by proving that the maximum product of distances for diameter-2 point sets can be found among convex polygons, providing improved constructions over regular -gons and demonstrating that a general characterization of extremal polygons is impossible for even orders.
This paper introduces the bicomplex Prabhakar derivative by extending fractional calculus to four-dimensional bicomplex spaces, establishing its fundamental operational properties and integral representations to provide a versatile framework for modeling complex phenomena with memory effects and multi-dimensional coupling.
This paper investigates matrices and operators satisfying the Kreiss condition with constants arbitrarily close to one, establishing refined lower bounds for power growth and demonstrating that specific variants of the condition guarantee similarity to a contraction when the spectrum touches the unit circle at a single point, utilizing a positivity argument involving the double-layer potential operator.
This paper empirically investigates the oscillatory behavior of determinants associated with Ramanujan functions on small primes, exploring potential regularities in their complex point sets as a means to address Lehmer's conjecture regarding the non-vanishing of Ramanujan's tau function.
This paper proves that, under mild assumptions, the Fano surfaces of lines on smooth cubic threefolds are the unique smooth subvarieties of abelian varieties whose Tannaka group for the convolution of perverse sheaves is an exceptional simple group, thereby significantly strengthening previous results on the Shafarevich conjecture.
This paper disproves the Perälä–Virtanen conjecture by constructing explicit radial symbols on Bergman and Fock spaces where a positive limit inferior of the Berezin transform fails to guarantee essential positivity, demonstrating that the Berezin liminf criterion is insufficient for radial Toeplitz operators in all complex dimensions.
This paper introduces the concept of strong regularity for subanalytic sheaves to establish microsupport estimates and derive initial value and division theorems for multi-microlocal objects, ultimately yielding a multi-microlocal version of Bochner's tube theorem for solutions of regular D-modules.
This paper investigates the shadowing phenomenon for composition operators on the Hardy space , specifically characterizing those induced by linear fractional self-maps of the unit disk that possess the positive shadowing property.
This paper investigates the parameter plane of cosine functions with a fixed critical point, classifying their hyperbolic components into three types and proving that their boundaries are Jordan curves and quasidisks using the para-puzzle method.
This paper establishes sharp bounds for the third-order Hankel, Toeplitz, and Hermitian-Toeplitz determinants of starlike functions associated with a balloon-shaped domain by utilizing coefficient inequalities and constructing suitable extremal functions to verify the results.
This paper establishes a complete proof of the Kobayashi-Hitchin correspondence for nef and big classes by introducing the concepts of adapted closed positive -currents and -adapted Hermitian-Yang-Mills metrics, thereby proving that a holomorphic vector bundle is slope polystable if and only if it admits such a metric, a result that extends to singular settings and yields new insights into projective flatness and the Bogomolov-Gieseker inequality.
This paper extends the non-abelian Hodge correspondence to compact Kähler spaces with klt singularities by establishing an equivalence between polystable Higgs bundles and semi-simple flat bundles on regular loci and proving a descent theorem for Higgs bundles along resolutions, ultimately yielding a quasi-uniformization theorem for projective klt varieties satisfying the orbifold Miyaoka-Yau equality.
This paper investigates the geometry of compact Kähler manifolds with partially semi-positive curvature by proving that such manifolds are rationally connected under specific positivity conditions and establishing structure theorems that classify them as either having high rational dimension or admitting a locally constant fibration with rationally connected fibers and a Ricci-flat base.
This paper investigates fluctuations in Coulomb gases under specific external potentials, proving that particle counts near spectral outposts follow an asymptotic Heine distribution while those near disconnected droplet components exhibit discrete normal fluctuations, ultimately characterizing general linear statistics as a sum of Gaussian and oscillatory discrete Gaussian fields.
This paper extends the complex multipoint Schwarz-Pick Lemma to the quaternionic setting of slice regular functions using iterated hyperbolic difference quotients, thereby deriving new estimates and providing an algorithm for constructing interpolating functions with real nodes.
This paper establishes that embedded infinite plane triangulations within ergodic scale-free environments converge to their circle packing and Riemann uniformization embeddings on a large scale, provided that specific moment and connectivity conditions are met.
This paper establishes an explicit second-order expansion for the volume dimension of the Julia sets of holomorphic skew products in as a perturbation parameter approaches zero, extending the classical Ruelle-McMullen results on Hausdorff dimension to non-conformal higher-dimensional dynamical systems.
This paper establishes that a hyperbolic polynomial with a connected Julia set is combinatorially rigid if and only if it is not of the "disjoint type," specifically proving that polynomials with attracting cycles attracting at least two critical points lack combinatorial rigidity.