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Distinguishing properties of weak slice conditions


Authors: Stephen M. Buckley and Alexander Stanoyevitch
Journal: Conform. Geom. Dyn. 7 (2003), 49-75
MSC (2000): Primary 30C65, 46E35
DOI: https://doi.org/10.1090/S1088-4173-03-00084-5
Published electronically: July 17, 2003
MathSciNet review: 1992037
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Abstract | References | Similar Articles | Additional Information

Abstract: The slice condition and the more general weak slice conditions are geometric conditions on Euclidean space domains which have evolved over the last several years as a tool in various areas of analysis. This paper explores some of the finer distinctive properties of the various weak slice conditions.


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  • [BB] Z. Balogh and S.M. Buckley, Geometric characterizations of Gromov hyperbolicity, to appear in Invent. Math.
  • [BHK] M. Bonk, J. Heinonen, and P. Koskela, Uniformizing Gromov hyperbolic spaces, Astérisque 270 (2001), viii+99 pp. MR 2003b:30024
  • [B] S.M. Buckley, Quasiconformal images of Holder domains, preprint.
  • [BK1] S.M. Buckley and P. Koskela, Sobolev-Poincaré implies John, Math. Research Letters 2 (1995), 577-593. MR 96i:46035
  • [BK2] S.M. Buckley and P. Koskela, Criteria for Imbeddings of Sobolev-Poincaré type, Internat. Math. Res. Notices (1996), 881-901. MR 98g:46041
  • [BO] S.M. Buckley and J. O'Shea, Weighted Trudinger-type inequalities, Indiana Univ. Math. J. 48 (1999), 85-114. MR 2001a:46031
  • [BS1] S.M. Buckley and A. Stanoyevitch, Weak slice conditions and Hölder imbeddings, J. London Math. Soc. 66 (2001), 690-706. MR 2002h:46051
  • [BS2] S.M. Buckley and A. Stanoyevitch, Weak slice conditions, product domains, and quasiconformal mappings, Rev. Math. Iberoam. 17 (2001), 1-37. MR 2003b:30025
  • [GM1] F.W. Gehring and O. Martio, Lipschitz classes and quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 203-219. MR 87b:30029
  • [GM2] F.W. Gehring and O. Martio, Quasiextremal distance domains and extension of quasiconformal mappings, J. Analyse Math. 45 (1985), 181-206. MR 87j:30043
  • [GO] F.W. Gehring and B. Osgood, Uniform domains and the quasihyperbolic metric, J. Analyse Math. 36 (1979), 50-74. MR 81k:30023
  • [HK] J. Heinonen and P. Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), 1-61. MR 99j:30025
  • [L] V. Lappalainen, $Lip_{h}$-extension domains, Ann. Acad. Sci. Fenn. Ser. A I Math. Diss. 56 (1985), 1-52. MR 87h:26021
  • [Mz] V.L. Maz$'$ya, Sobolev Spaces, Springer-Verlag, Berlin, 1985. MR 87g:46056
  • [V1] J. Väisälä, On the null-sets for extremal distances, Ann. Acad. Sci. Fenn. Ser. A I 322 (1962), 12pp. MR 26:5148
  • [V2] J. Väisälä, Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Mathematics 229, Springer-Verlag, Berlin, 1970. MR 56:12260
  • [V3] J. Väisälä, Uniform domains, Tohoku Math. J. 40 (1988), 101-118. MR 89d:30027
  • [V4] J. Väisälä, Quasiconformal mappings of cylindrical domains, Acta Math. 162 (1989), 201-225. MR 90f:30034
  • [V5] J. Väisälä, Relatively and inner uniform domains, Conf. Geom. Dyn. 2 (1998), 56-88. MR 99e:30014

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Additional Information

Stephen M. Buckley
Affiliation: Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, Ireland
Email: sbuckley@maths.may.ie

Alexander Stanoyevitch
Affiliation: Division of Mathematical Sciences, University of Guam, Mangilao, Guam 96923, USA
Email: alex@math.hawaii.edu

DOI: https://doi.org/10.1090/S1088-4173-03-00084-5
Received by editor(s): October 9, 2001
Received by editor(s) in revised form: April 10, 2003
Published electronically: July 17, 2003
Additional Notes: The first author was partially supported by Enterprise Ireland
Article copyright: © Copyright 2003 American Mathematical Society

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