66 papers
This paper resolves an open problem posed by Heittokangas, Ishizaki, Tohge, and Wen by completely characterizing all finite-order entire solutions of the differential-difference equation , where the coefficients are polynomials and .
This paper extends the harmonic analogue of Rouché's Theorem to non-circular critical curves to determine that the complex-valued harmonic function possesses either or zeros, which are confined to two explicit annuli under specific conditions on the parameters and .
This paper establishes a generalized version of Reshetnyak's theorem for quasiregular values mapping from generalized -manifolds with controlled geometry to Euclidean space , extending prior results by Kangasniemi and Onninen from the Euclidean setting.
This paper establishes that the space of infinite circle patterns in the Euclidean plane parameterized by discrete harmonic functions of finite Dirichlet energy forms an infinite-dimensional Hilbert manifold homeomorphic to the Sobolev space of half-differentiable functions, equipped with a Riemannian metric derived from a hyperbolic volume functional that relates to a symplectic form via an analogue of the Hilbert transform, thereby connecting these patterns to the Weil-Petersson class of the universal Teichmüller space.
This paper introduces rank-3 generalized Clifford manifolds, demonstrating that they canonically induce generalized hypercomplex structures and possess an integrable twistor space characterized by a natural Spin(3)-action and a generalized Nijenhuis tensor-based integrability condition.
This paper establishes that complex Hénon maps of a fixed degree are determined up to finitely many choices by their multiplier spectra, extending McMullen's classical rigidity theorem to higher dimensions by proving the nonexistence of stable algebraic families through precise asymptotic bounds on Lyapunov exponents.
This paper establishes that for endomorphisms of projective spaces or automorphisms of compact Kähler manifolds, the pull-backs of currents under iterates converge exponentially fast to Green currents when tested against -Hölder continuous observables with bounded mass.
This paper establishes the global Hölder continuity of solutions to the Dirichlet problem for the complex Monge-Ampère equation on strictly pseudoconvex domains or Hermitian manifolds, assuming the right-hand side belongs to and the boundary data are Hölder continuous.
This paper introduces the higher spin -operator associated with the Rarita-Schwinger operator, investigates its norm estimates, mapping properties, and adjoint, and applies these results to establish the existence and uniqueness of solutions for a higher spin Beltrami equation.
This paper classifies projective Legendrian subvarieties that are homogeneous under their stabilizers within the projectivized nilpotent orbits of complex semi-simple Lie algebras, specifically providing a classification of equivariant Legendrian embeddings of rational homogeneous spaces into adjoint varieties.
This paper establishes that the decomposition theorem components for contraction maps of torus actions of complexity one are intersection cohomology complexes of even codimensional subvarieties, leading to the vanishing of odd-dimensional intersection cohomology for rational complete varieties of this type and providing explicit formulas for the Betti numbers of affine trinomial hypersurfaces based on their defining equations.
This paper investigates two-variable compressions of shifts associated with rational inner functions on the bidisk, establishing their unitary equivalence to matrix-valued Toeplitz operators and demonstrating that while these symbols almost uniquely determine the underlying functions, the numerical ranges of the compressed shifts do not.
This paper demonstrates an asymmetry in uniqueness sets by constructing examples that fail to support measures with -summable Fourier coefficients while simultaneously supporting measures with rapidly decaying positive frequencies, thereby revealing a fundamental divergence between unilateral and bilateral uniqueness problems.
This paper characterizes the spectrum of Hausdorff operators acting on weighted Bergman and power weighted Hardy spaces defined over the upper half-plane.
This paper introduces a new collection of special functions associated with complex curves of genus 2 that relate to weight 2 -functions analogously to the Kleinian -function, with the distinct advantage of being well-defined for all such curves without requiring a Weierstrass point at infinity.
This paper reviews classical symmetry-based methods for solving the Levi problem and applies them to resolve the problem for generalized Hirzebruch manifolds and primary Hopf surfaces of non-diagonal type.
This paper establishes sharp uniform bounds on the eigenvalues of time-frequency localization operators and coherent state transform localizations near their spectral phase transition, revealing a qualitative difference in their decay rates where the former exhibits a logarithmic dependence while the latter decays quadratically.
This paper establishes that for sufficiently large , the non-real part of the closure of roots of restricted polynomials outside the unit disk is exactly the closure of a finite-capture locus, achieved by constructing canonical traps and proving uniform inclusion properties within a specific lens-shaped region.
This paper investigates the convergence of discrete exponential sums with positive exponents in neighborhoods of negative infinity, demonstrating that such sums can be effectively summed by grouping terms with similar exponents into "packages" to achieve massive cancellations, particularly when the sums are bounded within logarithmic neighborhoods.
This paper investigates the Laplace transform in general neighborhoods of to establish conditions for decomposing holomorphic functions into discrete sums of exponentials, addressing key properties such as continuity and resummation formulas.