Matches in SemOpenAlex for { <https://semopenalex.org/work/W3081148232> ?p ?o ?g. }
Showing items 1 to 80 of
80
with 100 items per page.
- W3081148232 abstract "This thesis falls naturally into two distinct parts. Both come under the general heading of the theory of conformal mapping though the later part incorporates work in potential theory. We first study the growth of means of the logarithmic derivative of a univalent function in the disc. Here results have been obtained by Hayman and by Baernstein and Brown. Hayman has shown that an elementary upper bound for the growth of these means is best possible in general. Later on, Baernstein and Brown showed that the means of certain classes of monotone slit mappings, including support points of the class S of normalised univalent functions, grow no faster than those of the Koebe function up to a multiplicative constant. The question remained open for unrestricted monotone slit mappings. We settle this question by constructing a monotone slit mapping the mean of whose logarithmic derivative grows faster than that of the Koebe function. Following this, we discuss some recent work by Burdzy on the boundary behaviour of positive harmonic functions in Lipschitz domains and applications of this work to the angular derivative problem. Burdzy obtains his results on the angular derivative by probabilistic methods. Rodin and Warschawski later gave a classical proof of part of Burdzy’s main result and related his criteria for the existence of an angular derivative to criteria which they had used previously. They were, however, unable to obtain a non-probabilistic proof of the full theorem. Using a new non-probabilistic method, we prove a theorem on the growth of positive harmonic functions vanishing near a boundary point of a Lipschitz domain. The plane case of this result and some special cases in space were proved by Burdzy in a series of articles. He went on to prove the full result in space in a later paper with R. J. Williams. Our result enables us to give an elementary proof of the remainder of Burdzy’s theorem on the angular derivative and so complements Rodin and Warschawski’s work. We complete our study of this problem by proving two further related results on the boundary behaviour of positive harmonic functions in Lipschitz domains. It is likely that the methods used will be helpful in problems of a similar nature." @default.
- W3081148232 created "2020-09-01" @default.
- W3081148232 creator A5079048921 @default.
- W3081148232 date "1988-01-01" @default.
- W3081148232 modified "2023-09-23" @default.
- W3081148232 title "Growth estimates for conformal mappings and for positive harmonic functions in space" @default.
- W3081148232 doi "https://doi.org/10.21954/ou.ro.0000f7f7" @default.
- W3081148232 hasPublicationYear "1988" @default.
- W3081148232 type Work @default.
- W3081148232 sameAs 3081148232 @default.
- W3081148232 citedByCount "0" @default.
- W3081148232 crossrefType "dissertation" @default.
- W3081148232 hasAuthorship W3081148232A5079048921 @default.
- W3081148232 hasConcept C105795698 @default.
- W3081148232 hasConcept C106159729 @default.
- W3081148232 hasConcept C111771559 @default.
- W3081148232 hasConcept C134306372 @default.
- W3081148232 hasConcept C14036430 @default.
- W3081148232 hasConcept C162324750 @default.
- W3081148232 hasConcept C202444582 @default.
- W3081148232 hasConcept C22324862 @default.
- W3081148232 hasConcept C2524010 @default.
- W3081148232 hasConcept C2834757 @default.
- W3081148232 hasConcept C33923547 @default.
- W3081148232 hasConcept C36649600 @default.
- W3081148232 hasConcept C39927690 @default.
- W3081148232 hasConcept C42747912 @default.
- W3081148232 hasConcept C49937458 @default.
- W3081148232 hasConcept C62354387 @default.
- W3081148232 hasConcept C627467 @default.
- W3081148232 hasConcept C78458016 @default.
- W3081148232 hasConcept C86803240 @default.
- W3081148232 hasConcept C98214594 @default.
- W3081148232 hasConceptScore W3081148232C105795698 @default.
- W3081148232 hasConceptScore W3081148232C106159729 @default.
- W3081148232 hasConceptScore W3081148232C111771559 @default.
- W3081148232 hasConceptScore W3081148232C134306372 @default.
- W3081148232 hasConceptScore W3081148232C14036430 @default.
- W3081148232 hasConceptScore W3081148232C162324750 @default.
- W3081148232 hasConceptScore W3081148232C202444582 @default.
- W3081148232 hasConceptScore W3081148232C22324862 @default.
- W3081148232 hasConceptScore W3081148232C2524010 @default.
- W3081148232 hasConceptScore W3081148232C2834757 @default.
- W3081148232 hasConceptScore W3081148232C33923547 @default.
- W3081148232 hasConceptScore W3081148232C36649600 @default.
- W3081148232 hasConceptScore W3081148232C39927690 @default.
- W3081148232 hasConceptScore W3081148232C42747912 @default.
- W3081148232 hasConceptScore W3081148232C49937458 @default.
- W3081148232 hasConceptScore W3081148232C62354387 @default.
- W3081148232 hasConceptScore W3081148232C627467 @default.
- W3081148232 hasConceptScore W3081148232C78458016 @default.
- W3081148232 hasConceptScore W3081148232C86803240 @default.
- W3081148232 hasConceptScore W3081148232C98214594 @default.
- W3081148232 hasLocation W30811482321 @default.
- W3081148232 hasOpenAccess W3081148232 @default.
- W3081148232 hasPrimaryLocation W30811482321 @default.
- W3081148232 hasRelatedWork W1021934921 @default.
- W3081148232 hasRelatedWork W1927751343 @default.
- W3081148232 hasRelatedWork W1987644943 @default.
- W3081148232 hasRelatedWork W2001730203 @default.
- W3081148232 hasRelatedWork W2004441218 @default.
- W3081148232 hasRelatedWork W2008407124 @default.
- W3081148232 hasRelatedWork W2026254254 @default.
- W3081148232 hasRelatedWork W2041828339 @default.
- W3081148232 hasRelatedWork W2051276402 @default.
- W3081148232 hasRelatedWork W2059550302 @default.
- W3081148232 hasRelatedWork W2094211535 @default.
- W3081148232 hasRelatedWork W2150884152 @default.
- W3081148232 hasRelatedWork W2278792150 @default.
- W3081148232 hasRelatedWork W2320313225 @default.
- W3081148232 hasRelatedWork W2328239358 @default.
- W3081148232 hasRelatedWork W2537596701 @default.
- W3081148232 hasRelatedWork W2804215844 @default.
- W3081148232 hasRelatedWork W30586996 @default.
- W3081148232 hasRelatedWork W3121948019 @default.
- W3081148232 hasRelatedWork W35130949 @default.
- W3081148232 isParatext "false" @default.
- W3081148232 isRetracted "false" @default.
- W3081148232 magId "3081148232" @default.
- W3081148232 workType "dissertation" @default.