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Distinguishing properties of weak slice conditions
Author(s):
Stephen
M.
Buckley;
Alexander
Stanoyevitch
Journal:
Conform. Geom. Dyn.
7
(2003),
49-75.
MSC (2000):
Primary 30C65, 46E35
Posted:
July 17, 2003
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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.
References:
-
- [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,
 -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
 -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:
10.1090/S1088-4173-03-00084-5
PII:
S 1088-4173(03)00084-5
Received by editor(s):
October 9, 2001
Received by editor(s) in revised form:
April 10, 2003
Posted:
July 17, 2003
Additional Notes:
The first author was partially supported by Enterprise Ireland
Copyright of article:
Copyright
2003,
American Mathematical Society
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