The free quasiworld. Freely quasiconformal and related maps in Banach spaces

• Autorzy: Jussi Väisälä
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1999
• Tom: 48
• Numer: 1
• Strony: 55-118

Daty

wydano

1999

Twórcy

autor

Jussi Väisälä

• Matematiikan laitos, Helsingin yliopisto, PL 4 (Yliopistonkatu 5), FIN-00014 Helsinki, Finland

Bibliografia

• [Al] P. Alestalo, Quasisymmetry in product spaces and uniform domains, Licentiate's thesis, University of Helsinki, 1991 (Finnish).
• [AG] K. Astala and F. W. Gehring, Injectivity, the BMO norm and the universal Teichmüller space, J. Analyse Math. 46 (1986), 16-57.
• [Ben] Y. Benyamini, The uniform classification of Banach spaces, Longhorn notes, University of Texas, 1984-85, 15-39.
• [BL] Y. Benyamini and J. Lindenstrauss, Geometric non-linear analysis, book to appear.
• [Bes] C. Bessaga, Every infinite-dimensional Hilbert space is diffeomorphic with its unit sphere, Bull. Acad. Polon. Sci. Ser. Sci. Mat. Astr. Phys. 14 (1966), 27-31.
• [BP] C. Bessaga and A. Pełczyński, Selected topics in infinite-dimensional topology, Polish Scientific Publishers, 1975.
• [BA] A. Beurling and L. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125-142.
• [CC] M. Cotlar and R. Cignoli, An introduction to functional analysis, North-Holland, 1974.
• [DS] D. A. De-Spiller, Equimorphisms and quasi-conformal mappings of the absolute, Soviet Math. Dokl. 11 (1970), 1324-1328.
• [ET] V. A. Efremovich and E. S. Tihomirova, Equimorphisms of hyperbolic spaces, Izv. Akad. Nauk SSSR 28 (1964), 1139-1144 (Russian).
• [Fe] H. Federer, Geometric measure theory, Springer-Verlag, 1969.
• [Ge1] F. W. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962), 353-393.
• [Ge2] F. W. Gehring, The Carathéodory convergence theorem for quasiconformal mappings, Ann. Acad. Sci. Fenn. Math. 336/11 (1963), 1-21.
• [Ge3] F. W. Gehring, Extension of quasiisometric embeddings of Jordan curves, Complex Variables 5 (1986), 245-263.
• [GM] F. W. Gehring and O. Martio, Quasiextremal distance domains and extension of quasiconformal mappings, J. Analyse Math. 45 (1985), 181-206.
• [GO] F. W. Gehring and B. G. Osgood, Uniform domains and the quasi-hyperbolic metric, J. Analyse Math. 36 (1979), 50-74.
• [GP] F. W. Gehring and B. P. Palka, Quasiconformally homogeneous domains, J. Analyse Math. 30 (1976), 172-199.
• [GV] F. W. Gehring and J. Väisälä, The coefficients of quasiconformality of domains in space, Acta Math. 114 (1965), 1-70.
• [Go] S. Gołąb, Quelques problèmes métriques de la géométrie de Minkowski, Prace Akademii Górniczej w Krakowie 6 (1932), 1-79 (Polish, French summary).
• [GR] V. M. Goldshtein and M. Rubin, Reconstruction of domains from their groups of quasiconformal autohomeomorphisms, Preprint, 1992.
• [HHM] K. Hag, P. Hag and O. Martio, Quasisimilarities; definitions, stability and extension, Rev. Roumaine Math. Pures Appl., to appear.
• [HK] J. Heinonen and P. Koskela, Definitions of quasiconformality, Invent. Math. 120 (1995), 61-79.
• [JLS] W. B. Johnson, J. Lindenstrauss and G. Schechtman, Banach spaces determined by their uniform structures, Geom. Funct. Anal. 6 (1996), 430-470.
• [Jo1] P. W. Jones, Extension theorems for BMO, Indiana Univ. Math. J. 29 (1980), 41-66.
• [Jo2] P. W. Jones, Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math. 147 (1981), 71-88.
• [Kü] R. Kühnau, Elementare Beispiele von möglichst konformen Abbildungen in der dreidimensionalen Raum, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 11 (1962), 729-732.
• [Lat] T. G. Latfullin, Criteria to the quasihyperbolicity of maps, Sibirsk. Mat. Zh. 37 (1996), 610-615 (Russian).
• [Lau] D. Laugwitz, Konvexe Mittelpunktsbereiche und normierte Räume, Math. Z. 61 (1954), 235-244.
• [LV] O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, Springer-Verlag, 1973.
• [Ma] O. Martio, Quasisimilarities, Rev. Roumaine Pures Appl. 36 (1991), 395-406.
• [MS] O. Martio and J. Sarvas, Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. Math. 4 (1979), 383-401.
• [Ri] S. Rickman, Quasiconformally equivalent curves, Duke Math. J. 36 (1969), 387-400.
• [Sc1] J. J. Schäffer, Inner diameter, perimeter and girth of spheres, Math. Ann. 173 (1967), 59-82.
• [Sc2] J. J. Schäffer, Geometry of spheres in normed spaces, Marcel Dekker, 1976.
• [TV1] P. Tukia and J. Väisälä, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Math. 5 (1980), 97-114.
• [TV2] P. Tukia and J. Väisälä, Lipschitz and quasiconformal approximation and extension, Ann. Acad. Sci. Fenn. Math. 6 (1981), 303-342.
• [TV3] P. Tukia and J. Väisälä, Quasiconformal extension from dimension n to n+1, Ann. of Math. 115 (1982), 331-348.
• [Vä1] J. Väisälä, Removable sets for quasiconformal mappings, J. Math. Mech. 19 (1969), 49-51.
• [Vä2] J. Väisälä, Lectures on n-dimensional quasiconformal mappings, Lecture notes in Math. 229, Springer-Verlag, 1971.
• [Vä3] J. Väisälä, Quasi-symmetric embeddings in euclidean spaces, Trans. Amer. Math. Soc. 264 (1981), 191-204.
• [Vä4] J. Väisälä, Quasimöbius maps, J. Analyse Math. 44 (1984/85), 218-234.
• [Vä5] J. Väisälä, Free quasiconformality in Banach spaces I, Ann. Acad. Sci. Fenn. Math. 15 (1990), 355-379.
• [Vä6] J. Väisälä, Free quasiconformality in Banach Spaces II, Ann. Acad. Sci. Fenn. Math. 16 (1991), 255-310.
• [Vä7] J. Väisälä, Free quasiconformality in Banach spaces III, Ann. Acad. Sci. Fenn. Math. 17 (1992), 393-408.
• [Vä8] J. Väisälä, Banach spaces and bilipschitz maps, Studia Math. 103 (1992), 291-294.
• [Vä9] J. Väisälä, Free quasiconformality in Banach spaces IV, Analysis and Topology, ed. by C. Andreian Cazacu et al., World Scientific, 1998.
• [Vu] M. Vuorinen, Conformal invariants and quasiregular mappings, J. Analyse Math. 45 (1985), 69-115.
• [Zo] V. A. Zorich, The theorem of M. A. Lavrent'ev on quasiconformal mappings, Math. USSR - Sbornik 3 (1967), 389-403.