Positive superharmonic functions and the Hölder continuity of conformal mappings

J. M. Anderson, A. Hinkkanen

Research output: Contribution to journalArticlepeer-review


We study the rate at which a positive superharmonic function u can tend to zero at a boundary point z 0of a plane domain G. In particular, if G is a quasidisk, and a > 0 is given, we show that the condition that lim inf «(z)/dist (z, dG) llct> 0 as z -* z 0in G for any such u is related to the condition that the conformal map/of the unit disk onto G withal) = z 0is Holder continuous with exponent a at the point 1. This leads us to consider the problem of finding the best exponent a for which /is Holder continuous. The answer depends on how we characterize quasidisks or quasicircles. In this connection we give a negative answer to a question of Nakki and Palka.

Original languageEnglish (US)
Pages (from-to)256-270
Number of pages15
JournalJournal of the London Mathematical Society
Issue number2
StatePublished - Apr 1989
Externally publishedYes


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