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Distortion of quasiconformal mappings with identity boundary values

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Abstract
Teichm¨uller’s classical mapping problem for plane domains concerns finding a lower bound for
the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise
fixed, maps the domain onto itself and maps a given point of the domain to another given point
of the domain. For a domain D ⊂ Rn, n > 2, we consider the class of all K-quasiconformal maps
of D onto itself with identity boundary values and Teichm¨uller’s problem in this context. Given
a map f of this class and a point x ∈ D, we show that the maximal dilatation of f has a lower
bound in terms of the distance of x and f(x). We improve recent results for the unit ball and
consider this problem in other more general domains. For instance, convex domains, bounded
domains and domains with uniformly perfect boundaries are studied.

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Informasi Detail

Judul Seri

J. London Math. Soc.

No. Panggil

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Penerbit

London : London Mathematical Society., 2014

Deskripsi Fisik

J. London Math. Soc. (2) 90 (2014) 637–653

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

MATEMATIKA

Info Detail Spesifik

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Pernyataan Tanggungjawab

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