The Schwarz lemma at the boundary

By Steven G. Krantz. 2010

75 citations recorded by the source corpus.

The most classical version of the Schwarz lemma involves the behaviour at the origin of a bounded, holomorphic function on the disc. Pick's version of the Schwarz lemma allows one to move the origin to other points of the disc. In this article we explore versions of the Schwarz lemma at a boundary point of a domain (not just the disc). Estimates on derivatives of the function, and other types of estimates as well, are considered. We review recent results of several authors, and present some new theorems as well.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d81b446d23632ec83eac613fe2238095a942e437

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In Applied Mathematics

1. M. Levenshtein
2. Fiana Jacobzon
3. David Shoikhet
4. Mark Elin

In Geometry and Topology

1. M. Levenshtein
2. Fiana Jacobzon
3. David Shoikhet
4. Mark Elin

Citations in the corpus

• The Schwarz Lemma: Rigidity and Dynamics (2014, methodology): “We formulate their results in a form compatible with the context (see also [33, 95, 114]).”