Critical sets of bounded analytic functions, zero sets of Bergman spaces and nonpositive curvature

DOI10.1112/PLMS/PDS054zbMath1273.30047arXiv1110.0275OpenAlexW3099743105MaRDI QIDQ4923032

Daniela Kraus

Publication date: 5 June 2013

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.0275

zbMATH Keywords

Bergman spaceconformal metricbounded analytic functioncritical setindestructible Blaschke productGauss curvature equationBerger-Nirenberg problem

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Spaces of bounded analytic functions of one complex variable (30H05) Bergman spaces and Fock spaces (30H20) Blaschke products (30J10)

Related Items (15)

Describing Blaschke Products by Their Critical Points ⋮ Critical points of solutions to a kind of linear elliptic equations in multiply connected domains ⋮ Critical points of solutions to a quasilinear elliptic equation with nonhomogeneous Dirichlet boundary conditions ⋮ Composition and decomposition of indestructible Blaschke products ⋮ Maximal Blaschke products ⋮ A new Schwarz-Pick lemma at the boundary and rigidity of holomorphic maps ⋮ Bounded projective functions and hyperbolic metrics with isolated singularities ⋮ Stable convergence of inner functions ⋮ Contracting properties of bounded holomorphic functions ⋮ Critical structures of inner functions ⋮ Prescribing inner parts of derivatives of inner functions ⋮ Uniqueness of critical points of solutions to the mean curvature equation with Neumann and Robin boundary conditions ⋮ Some generalizations of Ahlfors lemma ⋮ Critical Points, the Gauss Curvature Equation and Blaschke Products ⋮ Hyperbolic distortion, boundary behaviour and finite Blaschke products

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