Area, capacity and diameter versions of Schwarz's Lemma

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dc.creatorBurckel, Robert B.
dc.creatorMarshall, Donald E.
dc.creatorMinda, David
dc.creatorPoggi-Corradini, Pietro
dc.creatorRansford, Thomas J.
dc.date2008-01-23
dc.date.accessioned2026-07-07T08:56:06Z
dc.date.available2026-07-07T08:56:06Z
dc.descriptionThe now canonical proof of Schwarz's Lemma appeared in a 1907 paper of Carathéodory, who attributed it to Erhard Schmidt. Since then, Schwarz's Lemma has acquired considerable fame, with multiple extensions and generalizations. Much less known is that, in the same year 1907, Landau and Toeplitz obtained a similar result where the diameter of the image set takes over the role of the maximum modulus of the function. We give a new proof of this result and extend it to include bounds on the growth of the maximum modulus. We also develop a more general approach in which the size of the image is estimated in several geometric ways via notions of radius, diameter, perimeter, area, capacity, etc...
dc.identifierhttps://arxiv.org/abs/0801.3629
dc.identifierhttp://arxiv.org/abs/0801.3629
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146492
dc.subjectComplex Variables
dc.subjectClassical Analysis and ODEs
dc.subject30C80
dc.titleArea, capacity and diameter versions of Schwarz's Lemma
dc.typetext

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