Slice conditions and their applications

Buckley, Stephen M. (2003) Slice conditions and their applications. Report University of Jyväskylä Department of Mathematics and Statistics, 92. pp. 63-76. ISSN 1457-8905

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Slice-type conditions and their relatives have been used in a number of papers of the author and various collaborators to investigate a variety of problems in analysis including Sobolev-type imbedding theorems ([BuKo], [BuOS], [BuSt1], [Bu]), quasiconformal equivalence of domains ([BuSt2], [Bu]), and Gromov hyperbolicity ([BaBu]). Despite their usefulness, these conditions are still somewhat mysterious, but some recent research has helped to shed more light on them ([BaBu], [BuSt3], [BuDiSt]). There are quite a few varieties of slice conditions, partially reflecting the fact that di fferent applications require di erent conditions. In this paper, we defi ne some of these variants, discuss how they diff er from each other, and summarize their applications. Along the way, we encounter quite a few examples, counterexamples, and open questions. We discuss (strong) slice conditions and Gromov hyperbolicity in Section 2, weak slice conditions and their applications in Section 3, and some examples and useful lemmas in Section 4.

Item Type: Article
Keywords: Slice-type conditions; Sobolev-type imbedding theorems; Quasiconformal equivalence of domains; Gromov hyperbolicity.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1608
Depositing User: Prof. Stephen Buckley
Date Deposited: 21 Oct 2009 08:35
Journal or Publication Title: Report University of Jyväskylä Department of Mathematics and Statistics
Publisher: Jyväskylä Yliopisto, Matematiikan ja Tilastotieteen Laitos
Refereed: No

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