66 papers
This paper characterizes the real laminations of cubic polynomials on the tame boundaries of hyperbolic components of types (A), (B), and (C) by proving they are generated by the component's lamination and a single characteristic equivalence class, thereby demonstrating that all such hyperbolic cubic polynomials lack combinatorial rigidity.
This paper investigates the universal asymptotic behavior of correlations in two-dimensional Coulomb systems featuring an outpost Jordan curve, showing that these correlations along the outpost and outer boundary are governed by a reproducing kernel for a specific Hilbert space of analytic functions, thereby generalizing recent Szegő-type edge correlation results.
This paper constructs Green currents associated with the dominant eigenspaces of holomorphic correspondences on compact Kähler manifolds under specific dynamical degree conditions, establishes the log-Hölder continuity of their super-potentials, and proves the exponential equidistribution of positive closed currents toward the main Green current when the correspondence exhibits simple cohomological action and satisfies a local multiplicity assumption.
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.
The paper establishes a sharp inequality relating the Alexander-Taylor capacity to the functional capacity within complex Sobolev spaces on compact Kähler manifolds.
This paper investigates the convergence properties of M.V. Berry's superoscillating approximation to the truncated Weierstrass function, providing sharp error estimates and analyzing the associated double limits.
This paper establishes a necessary and sufficient condition for the finite Prony representability of linear viscoelastic models by analyzing the alignment of arithmetic pole lattices in the Mellin transform of the complex modulus, thereby providing a complete analytical taxonomy that classifies classical models as finitely representable and fractional or log-normal models as requiring infinite Prony ladders.
This paper establishes the conformal naturality of the Lieb isomorphism and the real-analyticity of the Douady-Earle section for Teichmüller spaces of closed sets in the Riemann sphere, utilizing these results to prove that families of Jordan curves with holomorphically varying marked points vary real-analytically as quasiconformal images.
This paper demonstrates that the Bloch and Landau constants for meromorphic functions with a simple pole in the unit disk are infinite, thereby refuting a recent conjecture and extending this result to functions with two simple poles.
The paper proves that any -pseudoconcave subset of the graph of a continuous function (or of locally representable as such a graph) can be decomposed into a disjoint union of -dimensional complex manifolds.
This paper presents methods for constructing two types of non-Runge Fatou-Bieberbach domains—proper open subsets biholomorphic to either or the ambient Stein manifold itself—within Stein manifolds possessing the density property, and provides concrete examples where these constructions are applicable.
This paper establishes that the Bergman kernel of a finite-volume quotient of a Hermitian manifold with bounded geometry is the average of the kernel over the discrete isometry group, and applies this result to Hermitian symmetric spaces to prove the non-vanishing of a broad class of relative Poincaré series, thereby extending previous findings to general locally symmetric spaces of finite volume.
This paper characterizes fractional Malliavin-Watanabe-Sobolev spaces for all by establishing a criterion based on the integrability and fractional differentiability properties of the -transform's Bargmann-Segal norm, thereby bridging Malliavin calculus with white noise analysis and providing practical tools for analyzing objects like Donsker's delta and self-intersection local times.
This paper resolves a long-standing open problem by establishing a universal central limit theorem for both smooth and numerical statistics of intersection currents arising from independent Gaussian holomorphic sections in arbitrary codimensions, thereby fully extending the 2010 Shiffman–Zelditch theorem through a novel geometric framework that adapts Wiener chaos and Feynman diagram techniques to random currents on complex manifolds.
This paper establishes sharp coefficient bounds for reciprocal antisymmetric polynomials with all zeros on the unit circle, provides explicit factorization formulas for the extremal cases involving derivatives of Chebyshev polynomials of the second kind, and derives a new identity expressing these derivatives as linear combinations of Chebyshev polynomials.
This paper investigates the deformation behavior of pseudo-effective canonical divisors and volumes of adjoint classes in Kähler families, establishing global stability results under specific conditions and confirming Siu's invariance of plurigenera conjecture for smooth Kähler threefolds.
This paper establishes the optimal regularity of the volume function on the big cone of a projective manifold and examines its regularity when restricted to segments moving in ample directions.
This paper characterizes the extreme and exposed points of the unit ball in the -norm for shift-invariant spaces generated by the Gaussian function and quasi shift-invariant spaces generated by the hyperbolic secant.
This paper establishes that localization operators on weighted Bergman spaces converge weakly to those on Fock spaces under natural scaling as the parameter , a result leveraged to derive sharp norm estimates for Toeplitz operators, analyze windowed Berezin transforms, and prove Szegő-type theorems.
This paper extends Masur and Minsky's result on the quasi-isometry between Teichmüller space and the curve graph to the -multicurve graph by electrifying the space along regions of small extremal length for curves, utilizing a new distance bound derived from intersection numbers.