Sobolev classes of Banach space-valued functions and quasiconformal mappings
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L. Ambrosio,Metric space valued functions of bounded variation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)17 (1990), 439–478.
L. Ambrosia and P. Tilli,Selected topics on “Analysis in Metric Spaces”, Appunti dei Corsi Tenuti da Docenti della Scuola, Scuola Normale Superiore, Pisa, 2000, 133 pp.
Z. Balogh and P. Koskela,Quasiconformality, quasisymmetry and removability in Loewner spaces, Duke Math. J.101 (2000), 554–577, with an appendix by J. Väisälä.
Y. Benjamini and J. Lindenstrauss,Geometric Nonlinear Functional Analysis, Volume 1, Vol. 48 of Colloquium Publications, Amer. Math. Soc., Providence, RI, 2000.
F. Bethuel,The approximation problem for Sobolev maps between two manifolds, Acta. Math.167 (1991), 153–206.
M. Bonk, J. Heinonen and P. Koskela,Uniformizing Gromov hyperbolic spaces, Astérisque270 (2001).
M. Bourdon and H. Pajot,Poincaré inequalities and quasiconformal structure on the boundaries of some hyperbolic buildings, Proc. Amer. Math. Soc.127 (1999), 2315–2324.
J. Cheeger,Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal.9 (1999), 428–517.
J. Diestel and J. J. Uhl,Vector Measures, American Mathematical Society, Providence, R.I., 1977, with a foreword by B. J. Pettis, Mathematical Surveys, No. 15.
H. Federer,Geometric Measure Theory, Vol. 153 ofDie Grundlehren der mathematischen Wissenschaften, Springer-Verlag, New York, 1969.
F. W. Gehring,The definitions and exceptional sets for quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I Math.281 (1960), 28pp.
F. W. Gehring,Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc.103 (1962),353–393.
F. W. Gehring,The L p -integrability of the partial derivatives of a quasiconformal mapping, Acta Math.130, (1973), 265–277.
F. W. Gehring,Lower dimensional absolute continuity properties of quasiconformal mappings, Math. Proc. Cambridge Philos. Soc.78 (1975), 81–93.
P. Hajłasz and P. Koskela,Sobolev met Poincaré Mem. Amer. Math. Soc.145 (2000), 688.
B. Hanson and J. Heinonen,An n-dimensional space that admits a Poincaré inequality but has no manifold points, Proc. Amer. Math. Soc.128 (2000), 3379–3390.
J. Heinonen,Calculus on Carnot groups, inFall School in Analysis (Jyväskylä, 1994), Vol. 68, Ber. Univ. Jyväskylä Math. Inst., Jyväskylä, 1995, pp. 1–31.
J. Heinonen, and A. Hinkkanen,Quasiconformal maps between compact polyhedra are quasisymmetric, Indiana Univ. Math. J.45 (1996), 997–1019.
J. Heinonen and P. Koskela,From local to global in quasiconformal structures, Proc. Natl. Acad. Sci. U.S.A.93 (1996), 554–556.
J. Heinonen and P. Koskela,Quasiconformal maps in metric spaces with controlled geometry, Acta Math.181 (1998), 1–61.
J. Heinonen and P. Koskela,A note on Lipschitz functions, upper gradients, and the Poincaré inequality, New Zealand J. Math.28 (1999), 37–42.
J. Jost,Generalized Dirichlet forms and harmonic maps, Calc. Var. Partial Differential Equations5 (1997), 1–19.
J. Jost, W. Kendall, U Mosco, M. Röckner and K.-T. Sturm,New Directions in Dirichlet Forms, American Mathematical Society, Providence, RI, 1998.
A. Korányi and H. M. Reimann,Quasiconformal mappings on the Heisenberg groups, Invent. Math.80 (1985), 309–338.
A. Koranyi and H. M. Reimann,Foundations for the theory of quasiconformal mappings on the Heisenberg group, Adv. Math.111 (1995), 1–87.
N. J. Korevaar and R. M. Schoen,Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom.1 (1993), 561–659.
P. Koskela and P. MacManus,Quasiconformal mappings and Sobolev spaces, Studia Math.131 (1998) 1–17.
P. Koskela, N. Shanmugalingam and H. Tuominen,Removable sets for the Poincaré inequality on metric spaces. Indiana Univ. Math. J.49 (2000), 333–352.
T. Laakso,Ahlfors Q-regular spaces with arbitary Q admitting weak Poincaré inequalities, Geom. Funct. Anal.10 (2000), 111–123.
U. Lang, B. Pavlović and V. Schroeder,Extensions of Lipschitz maps into Hadamard spaces, Geom. Funct. Anal.10 (2000), 1527–1553.
J. Maly and O. Martio,Lusin’s condition (N) and mappings of the class W 1, n, J. Reine Angew. Math.458 (1995), 19–36.
G. A. Margulis and G. D. Mostow,The differential of a quasi-conformal mapping of a Carnot-Caratheodory space, Geom. Funct. Anal.5 (1995), 402–433.
P. Mattila,Geometry of Sets and Measures in Euclidean Spaces Vol. 44 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1995.
G. D. Mostow,Quasiconformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math.34 (1968), 53–104.
G. D. Mostow,Strong Rigidity of Locally Symmetric Spaces, Annals of Mathematics Studies, No. 78, Princeton University Press, Princeton, N.J., 1973.
G. D. Mostow,A remark on quasiconformal mappings on Carnot groups, Michigan Math. J.41 (1994), 31–37.
P. Pansu,Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. (2),129 (1989), 1–60.
A. Ranjbar-Motlagh,Analysis on metric-measure spaces, Ph.D. thesis, New York University, 1998.
Y. G. Reshetnyak,The (N) condition for spatial mappings of the class W n, loc 1 , Sibirsk. Mat. Zh.28 (1987), 149–153.
Y. G. Reshetnyak,Sobolev classes of functions with values in a metric space, Sibirsk. Mat. Zh.38 (1997), 657–675.
S. Semmes,Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities, Selecta Math.2 (1996), 155–295.
N. Shanmugalingam,Harmonic functions on metric spaces, Illinois J. Math., to appear.
N. Shanmugalingam,Newtonian spaces: an extension of Sobolev spaces to metric measure spaces, PhD thesis, University of Michigan, 1999.
N. Shanmugalingam,Newtonian spaces: an extension of Sobolov spaces to metric measure spaces, Rev. Mat. Iberoamericana16 (2000), 243–279.
M. Troyanov,Approximating Lipschitz mappings and Sobolev mappings between metric spaces, in preparation.
P. Tukia and J. Väisälä,Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math.5 (1980), 97–114.
J. T. Tyson,Qusiconformality and quasisymmetry in metric measure spaces, Ann. Acad. Sci. Fenn. Ser. A I Math.23 (1998), 525–528.
J. T. Tyson,Geometric and analytic applications of a generalized definition of the conformal modulus, PhD thesis, University of Michigan, 1999.
J. T. Tyson,Analytic properties of locally quasisymmetric mappings from Euclidean domains, Indiana Univ. Math. J.49 (2000), 995–1016.
J. Väisälä,On quasiconformal mappings in space, Ann. Acad. Sci. Fenn. Ser. A I Math.298 (1961), 1–36.
J. Väisälä,Lectures on n-Dimensional Quasiconformal Mappings, Lecture Notes in Mathematics229, Springer-Verlag, Berlin, 1971.
J. Väisälä,Quasi-symmetric embeddings in Euclidean spaces, Trans. Amer. Math. Soc.264 (1981), 191–204.
J. Väisälä,Questions on quasiconformal maps in space, inQuasiconformal Mappings and Analysis (Ann Arbor, MI, 1995), Springer, New York, 1998, pp. 369–374.