Generalized John disks

• Autorzy: Chang-Yu Guo , Pekka Koskela
• Języki publikacji: EN

Abstrakty

EN

We establish the basic properties of the class of generalized simply connected John domains.

Słowa kluczowe

EN

Conformal mapping; Hyperbolic geodesic; John domain; Inner uniform domain

Kategorie tematyczne

• 30C62: Quasiconformal mappings in the plane
• 30C65: Quasiconformal mappings in 𝐑 n , other generalizations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 2
• Strony: 349-361

Daty

wydano

2014-02-01

online

2013-11-21

Twórcy

autor

Chang-Yu Guo

• University of Jyväskylä

autor

Pekka Koskela

• University of Jyväskylä

Bibliografia

• [1] Astala K., Iwaniec T., Martin G., Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane, Princeton Math. Ser., 48, Princeton University Press, Princeton, 2009
• [2] Balogh Z., Volberg A., Geometric localization, uniformly John property and separated semihyperbolic dynamics, Ark. Mat., 1996, 34(1), 21–49 http://dx.doi.org/10.1007/BF02559505
• [3] Buckley S., Koskela P., Sobolev-Poincaré implies John, Math. Res. Lett., 1995, 2(5), 577–593 http://dx.doi.org/10.4310/MRL.1995.v2.n5.a5
• [4] Gehring F.W., Hayman W.K., An inequality in the theory of conformal mapping, J. Math. Pures Appl., 1962, 41, 353–361
• [5] Gehring F.W., Palka B.P., Quasiconformally homogeneous domains, J. Analyse Math., 1976, 30, 172–199 http://dx.doi.org/10.1007/BF02786713
• [6] Guo C.Y., Generalized quasidisks and conformality II, preprint available at http://arxiv.org/abs/1311.1967
• [7] Guo C.Y., Koskela P., Takkinen J., Generalized quasidisks and conformality, Publ. Mat., 2014, 58(1) (in press)
• [8] Hakobyan H., Herron D.A., Euclidean quasiconvexity, Ann. Acad. Sci. Fenn. Math., 2008, 33(1), 205–230
• [9] John F., Rotation and strain, Comm. Pure Appl. Math., 1961, 14(3), 391–413 http://dx.doi.org/10.1002/cpa.3160140316
• [10] Koskela P., Lectures on quasiconformal and quasisymmetric mappings, Jyväskylä Lectures in Mathematics, 1, preprint available at http://users.jyu.fi/_pkoskela/quasifinal.pdf
• [11] Martio O., John domains, bi-Lipschitz balls and Poincaré inequality, Rev. Roumaine Math. Pures Appl., 1988, 33(1–2), 107–112
• [12] Martio O., Sarvas J., Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. Math., 1979, 4(2), 383–401
• [13] Näkki R., Väisälä J., John disks, Exposition. Math., 1991, 9(1), 3–43
• [14] Nieminen T., Generalized mean porosity and dimension, Ann. Acad. Sci. Fenn. Math., 2006, 31(1), 143–172
• [15] Pommerenke Ch., Boundary Behaviour of Conformal Maps, Grundlehren Math. Wiss., 299, Springer, Berlin, 1992 http://dx.doi.org/10.1007/978-3-662-02770-7
• [16] Reshetnyak Yu.G., Integral representations of differentiable functions in domains with nonsmooth boundary, Siberian Math. J., 1980, 21(6), 833–839 http://dx.doi.org/10.1007/BF00968470
• [17] Smith W., Stegenga D.A., Hölder domains and Poincaré domains, Trans. Amer. Math. Soc., 1990, 319(1), 67–100
• [18] Takkinen J., Mappings of finite distortion: formation of cusps II, Conform. Geom. Dyn., 2007, 11, 207–218 http://dx.doi.org/10.1090/S1088-4173-07-00170-1

Identyfikatory

DOI

10.2478/s11533-013-0344-3