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A Distortion Theorem for Quadrature Domains for Harmonic Functions

✍ Scribed by Björn Gustafsson

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
168 KB
Volume
202
Category
Article
ISSN
0022-247X

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✦ Synopsis

We prove that any finitely connected domain in the plane can be distorted so that it becomes ''graviequivalent'' to a signed measure with arbitrarily small support. Precisely: if D ; ‫ރ‬ is a bounded, finitely connected domain with analytic Ž . boundary then for any a g D and r ) 0, ) 0 with B a, r q ; D there exists a < Ž . < Ž . univalent function g in D with g z y zz g D and a signed measure Ž . with support in B a, r such that for every integrable harmonic function h in Ž . ⍀[g D we have H h dx dy s Hh d.

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