The quasiconformal subinvariance property of John domains in \({\mathbb {R}}^n\) and its applications

详细信息    查看全文

• 作者：Manzi Huang ; Yaxiang Li ; Saminathan Ponnusamy ; Xiantao Wang
• 关键词：30C65 ; 30F45 ; 30C20
• 刊名：Mathematische Annalen
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：363
• 期：1-2
• 页码：549-615
• 全文大小：1,397 KB
• 参考文献：1.Ahlfors, L.V.: Quasiconformal reflections. Acta Math. 109, 291鈥?01 (1963)MATH MathSciNet CrossRef
  2.Beardon, A.F.: The Apollonian metric of a domain in \({\mathbb{R}}^{n}\) . In: Quasiconformal Mappings and Analysis, pp. 91鈥?08. Springer-Velag, Berlin (1998)
  3.Balogh, Z.M., Koskala, P.: Quasiconformality, quasisymmetry and removability in L枚ewner spaces. Duke Math. J. 101, 554鈥?77 (2000)MathSciNet
  4.Bonk, M., Heinonen, J., Koskela, P.: Uniformizing Gromov hyperbolic spaces. Ast茅risque 270, 99 (2001)MathSciNet
  5.Bonk, M., Kleiner, B.: Quasisymmetric parametrizations of two-dimensional metric spheres. Invent. Math. 150, 127鈥?83 (2002)MATH MathSciNet CrossRef
  6.Bonk, M., Merenkov, S.: Quasisymmetric rigidity of square Sierpinski carpets. Ann. Math. 177, 591鈥?43 (2013)MATH MathSciNet CrossRef
  7.Broch, O.J.: Geometry of John disks. Ph.D. Thesis, NTNU (2004)
  8.Fern谩ndez, J.L., Heinonen, J., Martio, O.: Quasilines and quasiconformal mappings. J. Anal. Math. 52, 117鈥?32 (1989)MATH CrossRef
  9.Ghamsari, M., Na茂kki, R., V盲is盲l盲, J.: John disks and extension of maps. Monatsh. Math. 117, 63鈥?4 (1994)MATH MathSciNet CrossRef
  10.Gehring, F.W.: Uniform domains and the ubiquitous quasidisk. Jahresber. Deutsch. Math. Verein 89, 88鈥?03 (1987)MATH MathSciNet
  11.Gehring, F.W., Martio, O.: Quasiextremal distance domains and extension of quasiconformal mappings. J. Anal. Math. 45, 181鈥?06 (1985)MATH MathSciNet CrossRef
  12.Gehring, F.W., Osgood, B.G.: Uniform domains and the quasi-hyperbolic metric. J. Anal. Math. 36, 50鈥?4 (1979)MATH MathSciNet CrossRef
  13.Gehring, F.W., Palka, B.P.: Quasiconformally homogeneous domains. J. Anal. Math. 30, 172鈥?99 (1976)MATH MathSciNet CrossRef
  14.H盲st枚, P.: The Apollonian metric: uniformity and quasiconvexity. Ann. Acad. Sci. Fenn. Ser. Math. 28, 385鈥?14 (2003)MATH
  15.Heinonen, J.: Quasiconformal mappings onto John domains. Rev. Math. Iber. 5, 97鈥?23 (1989)MATH MathSciNet CrossRef
  16.Heinonen, J.: Lectures on Analysis on Metric Spaces. Universitext. Springer-Verlag, New York (2001)MATH CrossRef
  17.Heinonen, J., Koskela, P.: Quasiconformal maps in metric spaces with controlled geometry. Acta Math. 181, 1鈥?1 (1998)MATH MathSciNet CrossRef
  18.Heinonen, J., Rohde, S.: The Gehring-Hayman inequality for quasihyperbolic geodesics. Math. Proc. Camb. Philos. Soc. 114, 393鈥?05 (1993)MATH MathSciNet CrossRef
  19.Herron, D.A.: Conformal deformations of uniform L枚ewner spaces. Math. Proc. Camb. Philos. Soc. 136, 325鈥?60 (2004)MATH MathSciNet CrossRef
  20.Huang, M., Li, Y.: Decomposition properties of John domains in real normed vector spaces. J. Math. Anal. Appl. 388, 191鈥?97 (2012)MATH MathSciNet CrossRef
  21.Huang, M., Li, Y., Vuorinen, M., Wang, X.: On quasim枚bius maps in real Banach spaces. Israel J. Math. 198, 467鈥?86 (2013)MATH MathSciNet CrossRef
  22.Huang, M., Wang, X.: Uniform domains and uniform domain decomposition property in real normed vector spaces. Math. Scand. 113, 128鈥?42 (2013)MATH MathSciNet
  23.John, F.: Rotation and strain. Commun. Pure. Appl. Math. 14, 391鈥?13 (1961)MATH CrossRef
  24.Jones, P.W.: Extension theorems for BMO. Indiana Univ. Math. J. 29, 41鈥?6 (1980)MATH MathSciNet CrossRef
  25.Jones, P.W.: Quasiconformal mappings and extendability of functions in Sobolev spaces. Acta Math. 147, 71鈥?8 (1981)MATH MathSciNet CrossRef
  26.Kim, K., Langmeyer, N.: Harmonic measure and hyperbolic distance in John disks. Math. Scand. 83, 283鈥?99 (1998)MATH MathSciNet
  27.Li, Y., Wang, X.: Unions of John domains and uniform domains in real normed vector spaces. Ann. Acad. Sci. Fenn. Ser. Math. 35, 627鈥?32 (2010)MATH CrossRef
  28.Martio, O.: Definitions of uniform domains. Ann. Acad. Sci. Fenn. Ser. A I Math. 5, 197鈥?05 (1980)MATH MathSciNet CrossRef
  29.Martio, O., Sarvas, J.: Injectivity theorems in plane and space. Ann. Acad. Sci. Fenn. Ser. A I Math. 4, 383鈥?01 (1978)MathSciNet CrossRef
  30.N盲kki, R., V盲is盲l盲, J.: John disks. Expo. Math. 9, 3鈥?3 (1991)MATH
  31.Tyson, J.T.: Metric and geometric quasiconformality in Ahlfors regular L枚ewner spaces. Conformal Geom. Dyn. 5, 21鈥?3 (2001)MATH MathSciNet CrossRef
  32.V盲is盲l盲, J.: Lectures on n-Dimensional Quasiconformal Mappings. Springer-Verlag, Berlin (1971)MATH
  33.V盲is盲l盲, J.: Quasi-symmetric embeddings in Euclidean spaces. Trans. Am. Math. Soc. 264, 191鈥?04 (1981)MATH CrossRef
  34.V盲is盲l盲, J.: Quasim枚bius maps. J. Anal. Math. 44, 218鈥?34 (1985)MATH CrossRef
  35.V盲is盲l盲, J.: Uniform domains. T么hoku Math. J. 40, 101鈥?18 (1988)MATH CrossRef
  36.V盲is盲l盲, J.: Quasiconformal maps of cylindrical domains. Acta Math. 162, 201鈥?25 (1989)MATH MathSciNet CrossRef
  37.V盲is盲l盲, J.: Free quasiconformality in Banach spaces. II. Ann. Acad. Sci. Fenn. Ser. A I Math. 16, 255鈥?10 (1991)MATH CrossRef
  38.V盲is盲l盲, J.: Free quasiconformality in Banach spaces. III. Ann. Acad. Sci. Fenn. Ser. A I Math. 17, 393鈥?08 (1992)MATH CrossRef
  39.V盲is盲l盲, J.: Free Quasiconformality in Banach Spaces. IV, Analysis and Topology, pp. 697鈥?17. World Sci. Publ., River Edge, NJ (1998)
  40.V盲is盲l盲, J.: Relatively and inner uniform domains. Conformal Geom. Dyn. 2, 56鈥?8 (1998)MATH CrossRef
  41.V盲is盲l盲, J.: The free quasiworld: freely quasiconformal and related maps in Banach spaces. In: Quasiconformal Geometry and Dynamics (Lublin 1996), Banach Center Publications, vol. 48, pp. 55鈥?18. Polish Academy of Science, Warsaw (1999)
  42.Vuorinen, M.: Conformal invariants and quasiregular mappings. J. Anal. Math. 45, 69鈥?15 (1985)MATH MathSciNet CrossRef
  43.Vuorinen, M.: Conformal Geometry and Quasiregular Mappings (Monograph). Lecture Notes in Math. vol. 1319, p. 208. Springer-Verlag, Berlin (1988)
  
• 作者单位：Manzi Huang (1)
  Yaxiang Li (2)
  Saminathan Ponnusamy (3)
  Xiantao Wang (4)
  
  1. Department of Mathematics, Hunan Normal University, Changsha, 410081, Hunan, People鈥檚 Republic of China
  2. College of Science, Central South University of Forestry and Technology, Changsha, 410004, Hunan, People鈥檚 Republic of China
  3. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security), MGR Knowledge City, CIT Campus, Taramani, Chennai, 600 113, India
  4. Department of Mathematics, Shantou University, Shantou, 515063, Guangdong, People鈥檚 Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

The main aim of this paper is to give a complete solution to one of the open problems, raised by Heinonen from 1989, concerning the subinvariance of John domains under quasiconformal mappings in \({\mathbb {R}}^n\). As application, the quasisymmetry of quasiconformal mappings is discussed. Mathematics Subject Classification 30C65 30F45 30C20