Buckley, Stephen M.
Slice conditions and their applications.
Report University of Jyväskylä Department of Mathematics and Statistics, 92.
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 different applications require dierent conditions. In this paper, we define
some of these variants, discuss how they differ 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.
||Slice-type conditions; Sobolev-type imbedding theorems; Quasiconformal equivalence of domains; Gromov hyperbolicity.
||Science & Engineering > Mathematics
Prof. Stephen Buckley
||21 Oct 2009 08:35
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||Report University of Jyväskylä Department of Mathematics and Statistics
||Jyväskylä Yliopisto, Matematiikan ja Tilastotieteen Laitos
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