The oscillation of harmonic and quasiregular mappings |
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| Authors: | J.M. Anderson A. Hinkkanen |
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| Affiliation: | (1) Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK , GB;(2) Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 West Green Street, Urbana, IL 61801, USA , US |
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| Abstract: | Abstract. If u(z) is harmonic in with and we set A result is obtained which shows, in particular that if and then a bound for can be obtained in terms of for a suitable constant , so that the logarithm of the oscillation has an approximate convexity property. The proof uses classical inequalities of Hadamard and Borel–Carathéodory and this suggests a generalization to quasiregular mappings in . Such results are obtained, though necessarily in a less precise form because of the lack of good explicit estimates for -harmonic measures in spherical ring domains. Received: 9 November 2000 / Published online: 18 January 2002 |
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