The radial behavior of a quasiconformal mapping

previous :: next

The radial behavior of a quasiconformal mapping

Pekka Koskela

Source: Duke Math. J. Volume 74, Number 3 (1994), 667-679.

First Page: Show

Primary Subjects: 30C65

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288420
Mathematical Reviews number (MathSciNet): MR1277949
Zentralblatt MATH identifier: 0834.30022
Digital Object Identifier: doi:10.1215/S0012-7094-94-07424-3

back to Table of Contents

References

[A] P. Assouad, Plongements lipschitziens dans $\bf R\spn$, Bull. Soc. Math. France 111 (1983), no. 4, 429–448.

Mathematical Reviews (MathSciNet): MR86f:54050

Zentralblatt MATH: 0597.54015

[AG] K. Astala and F. W. Gehring, Quasiconformal analogues of theorems of Koebe and Hardy-Littlewood, Michigan Math. J. 32 (1985), no. 1, 99–107.

Mathematical Reviews (MathSciNet): MR86j:30029

Zentralblatt MATH: 0574.30027

Digital Object Identifier: doi:10.1307/mmj/1029003136

Project Euclid: euclid.mmj/1029003136

[AH] K. Astala and J. Heinonen, On quasiconformal rigidity in space and plane, Ann. Acad. Sci. Fenn. Ser. A I Math. 13 (1988), no. 1, 81–92.

Mathematical Reviews (MathSciNet): MR90d:30055

Zentralblatt MATH: 0633.30021

[AK] K. Astala and P. Koskela, Quasiconformal mappings and global integrability of the derivative, J. Anal. Math. 57 (1991), 203–220.

Mathematical Reviews (MathSciNet): MR94c:30026

Zentralblatt MATH: 0772.30022

[B] J. Bourgain, On the Hausdorff dimension of harmonic measure in higher dimension, Invent. Math. 87 (1987), no. 3, 477–483.

Mathematical Reviews (MathSciNet): MR88b:31004

Zentralblatt MATH: 0616.31004

Digital Object Identifier: doi:10.1007/BF01389238

[CMG] J. G. Clunie and T. H. MacGregor, Radial growth of the derivative of univalent functions, Comment. Math. Helv. 59 (1984), no. 3, 362–375.

Mathematical Reviews (MathSciNet): MR86c:30035

Zentralblatt MATH: 0549.30012

Digital Object Identifier: doi:10.1007/BF02566357

[DS] G. David and S. Semmes, Analysis of and on uniformly rectifiable sets, to appear.

Mathematical Reviews (MathSciNet): MR1251061

Zentralblatt MATH: 0832.42008

[GM] F. W. Gehring and O. Martio, Lipschitz classes and quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 203–219.

Mathematical Reviews (MathSciNet): MR87b:30029

Zentralblatt MATH: 0584.30018

[H] J. Heinonen, Boundary accessibility and elliptic harmonic measures, Complex Variables Theory Appl. 10 (1988), no. 4, 273–282.

Mathematical Reviews (MathSciNet): MR90i:31015

Zentralblatt MATH: 0619.30032

[HK] J. Heinonen and P. Koskela, The boundary distortion of a quasiconformal mapping, to appear in Pacific J. Math.

Mathematical Reviews (MathSciNet): MR1285566

Zentralblatt MATH: 0813.30017

Project Euclid: euclid.pjm/1102621914

[HM] J. Heinonen and O. Martio, Estimates for $F$-harmonic measures and Øksendal's theorem for quasiconformal mappings, Indiana Univ. Math. J. 36 (1987), no. 3, 659–683.

Mathematical Reviews (MathSciNet): MR90c:30035

Zentralblatt MATH: 0643.35022

Digital Object Identifier: doi:10.1512/iumj.1987.36.36038

[JM] P. W. Jones and N. G. Makarov, Density properties of harmonic measure, to appear in Ann. of Math. (2).

Mathematical Reviews (MathSciNet): MR1356778

Zentralblatt MATH: 0842.31001

Digital Object Identifier: doi:10.2307/2118551

JSTOR: links.jstor.org

[K1] P. Koskela, An inverse Sobolev lemma, to appear in Rev. Mat. Iberoamericana.

Mathematical Reviews (MathSciNet): MR1271759

Zentralblatt MATH: 0795.30020

[K2] P. Koskela, The degree of regularity of a quasiconformal mapping, to appear in Proc. Amer. Math. Soc.

Mathematical Reviews (MathSciNet): MR1204381

Zentralblatt MATH: 0814.30015

Digital Object Identifier: doi:10.2307/2160752

JSTOR: links.jstor.org

[LP] A. J. Lohwater and G. Piranian, On the derivative of a univalent function, Proc. Amer. Math. Soc. 4 (1953), 591–594.

Mathematical Reviews (MathSciNet): MR15,114g

Zentralblatt MATH: 0050.30202

Digital Object Identifier: doi:10.2307/2032531

[M1] N. G. Makarov, On the distortion of boundary sets under conformal mappings, Proc. London Math. Soc. (3) 51 (1985), no. 2, 369–384.

Mathematical Reviews (MathSciNet): MR87d:30012

Zentralblatt MATH: 0573.30029

Digital Object Identifier: doi:10.1112/plms/s3-51.2.369

[M2] N. G. Makarov, Conformal mapping and Hausdorff measures, Ark. Mat. 25 (1987), no. 1, 41–89.

Mathematical Reviews (MathSciNet): MR89g:30044

Zentralblatt MATH: 0639.30008

Digital Object Identifier: doi:10.1007/BF02384436

[MM] J. Maly and O. Martio, Lusin's condition $(N)$ and mappings of the class $W^ 1,n$, to appear.

[NP] R. Näkki and B. Palka, Asymptotic values and Hölder continuity of quasiconformal mappings, J. Analyse Math. 48 (1987), 167–178.

Mathematical Reviews (MathSciNet): MR89d:30026

Zentralblatt MATH: 0633.30022

Digital Object Identifier: doi:10.1007/BF02790327

[Ø1] B. K. Øksendal, Null sets for measures orthogonal to $R(X)$, Amer. J. Math. 94 (1972), 331–342.

Mathematical Reviews (MathSciNet): MR47:835

Zentralblatt MATH: 0255.46042

Digital Object Identifier: doi:10.2307/2374624

JSTOR: links.jstor.org

[Ø2] B. Øksendal, Brownian motion and sets of harmonic measure zero, Pacific J. Math. 95 (1981), no. 1, 179–192.

Mathematical Reviews (MathSciNet): MR83c:60106

Zentralblatt MATH: 0493.31001

Project Euclid: euclid.pjm/1102735538

[P] Ch. Pommerenke, On the boundary continuity of conformal maps, Pacific J. Math. 120 (1985), no. 2, 423–430.

Mathematical Reviews (MathSciNet): MR87c:30011

Zentralblatt MATH: 0534.30008

Project Euclid: euclid.pjm/1102703424

[S] S. Semmes, Bi-Lipschitz mappings and strong $A\sb \infty$ weights, Ann. Acad. Sci. Fenn. Ser. A I Math. 18 (1993), no. 2, 211–248.

Mathematical Reviews (MathSciNet): MR95g:30032

Zentralblatt MATH: 0742.46010

[SS] W. Smith and D. A. Stegenga, Exponential integrability of the quasi-hyperbolic metric on Hölder domains, Ann. Acad. Sci. Fenn. Ser. A I Math. 16 (1991), no. 2, 345–360.

Mathematical Reviews (MathSciNet): MR93b:30016

Zentralblatt MATH: 0725.46024

[T] D. A. Trotsenko, Continuation from a domain and the approximation of space quasiconformal mappings with small dilatation coefficient, Soviet Math. Dokl. 27 (1983), 777–780.

Zentralblatt MATH: 0541.30007

[V1] J. Väisälä, Lectures on $n$-dimensional quasiconformal mappings, Springer-Verlag, Berlin, 1971.

Mathematical Reviews (MathSciNet): MR56:12260

Zentralblatt MATH: 0221.30031

[V2] J. Väisälä, Quasi-Möbius maps, J. Analyse Math. 44 (1984/85), 218–234.

Mathematical Reviews (MathSciNet): MR87f:30059

Digital Object Identifier: doi:10.1007/BF02790198

[V3] J. Väisälä, Quasiconformal maps and positive boundary measure, Analysis 9 (1989), no. 1-2, 205–216.

Mathematical Reviews (MathSciNet): MR91k:30058

Zentralblatt MATH: 0674.30018

[Vu] M. Vuorinen, Conformal geometry and quasiregular mappings, Lecture Notes in Mathematics, vol. 1319, Springer-Verlag, Berlin, 1988.

Mathematical Reviews (MathSciNet): MR89k:30021

Zentralblatt MATH: 0646.30025

[Z] W. P. Ziemer, Weakly differentiable functions, Graduate Texts in Mathematics, vol. 120, Springer-Verlag, New York, 1989.

Mathematical Reviews (MathSciNet): MR91e:46046

Zentralblatt MATH: 0692.46022

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?