Another look at the Burns-Krantz theorem

DOI10.1007/s11854-008-0030-8zbMath1154.30021arXivmath/0702377OpenAlexW1994811035MaRDI QIDQ948857

David M. Shoikhet

Publication date: 16 October 2008

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702377

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80)

Related Items (21)

Schwarzian derivative and covering arcs of a pencil of circles by holomorphic functions ⋮ Complex geodesics and complex Monge-Ampère equations with boundary singularity ⋮ Parametric representation of infinitesimal generators on the polydisk ⋮ Rigidity and parametric embedding of semi-complete vector fields on the unit disk ⋮ Ahlfors-Beurling conformal invariant and relative capacity of compact sets ⋮ A new Schwarz-Pick lemma at the boundary and rigidity of holomorphic maps ⋮ Non-tangential Burns-Krantz rigidity ⋮ Boundary distortion and the Schwarzian derivative of a univalent function in a circular annulus ⋮ The Burns-Krantz type rigidity for domains with corners ⋮ Nonlinear resolvent and rigidity of holomorphic mappings ⋮ A Burns–Krantz-type Theorem for Pseudo-contractive Mappings ⋮ Boundary behavior of infinitesimal generators in the unit ball ⋮ The Schwarz lemma at the boundary ⋮ Boundary behavior and rigidity of semigroups of holomorphic mappings ⋮ Parabolic type semigroups: asymptotics and order of contact ⋮ Several inequalities for the Schwarzian derivative of a bounded analytic function ⋮ Nonlinear resolvent and rigidity of holomorphic mappings ⋮ Производная Шварца и покрытие дуг пучка окружностей голоморфными функциями ⋮ Pseudo-contractions, rigidity, fixed points and related questions ⋮ Semigroups versus evolution families in the Loewner theory ⋮ The Schwarz Lemma: Rigidity and Dynamics

Cites Work

• A Julia-Carathéodory theorem for hyperbolically monotone mappings in the Hilbert ball
• The infinitesimal generators of semigroups of holomorphic maps
• Semigroups of analytic functions and composition operators
• Semigroups and generators on convex domains with the hyperbolic metric
• Composition operators and classical function theory
• A new rigidity result for holomorphic maps
• Identity principles for commuting holomorphic self-maps of the unit disc
• Generation theory for semigroups of holomorphic mappings in Banach spaces
• Parametric representations of semi-complete vector fields on the unit balls in \(\mathbb{C}^ n\) and in Hilbert space.
• A rigidity theorem for composition operators on certain Bergman spaces
• Infinitesimal generators associated with semigroups of linear fractional maps
• Analytic flows on the unit disk: angular derivatives and boundary fixed points
• A continuous form of Schwarz's lemma in normed linear spaces
• Cyclic phenomena for composition operators
• Rigidity at the boundary for holomorphic self-maps of the unit disk
• Second angular derivatives and parabolic iteration in the unit disk
• Commuting semigroups of holomorphic mappings
• Rigidity of Holomorphic Mappings and a New Schwarz Lemma at the Boundary
• Commuting holomorphic maps of the unit disc
• Metric domains, holomorphic mappings and nonlinear semigroups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Another look at the Burns-Krantz theorem