Proceedings of the American Mathematical Society

Author(s): S. Rohde
Journal: Proc. Amer. Math. Soc. 135 (2007), 1169-1173.
MSC (2000): Primary 30C35
Posted: November 13, 2006
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Abstract: In this note, we provide an answer to a question of D. Mejia and Chr. Pommerenke, by constructing a hyperbolically convex subdomain

of the unit disc $\mathbb{D}$ so that the conformal map from $\mathbb{D}$ to

maps a set of dimension 0 on $\partial\mathbb{D}$ to a set of dimension

1.: J. L. Fernández, J. Heinonen, O. Martio Quasilines and conformal mappings, J. Analyse Math. 52 (1989), 117-132. MR 0981499 (90a:30017)
2.: W. C. Ma, D. Minda, Hyperbolically convex functions, Ann. Polon. Math. 60 (1994), no. 1, 81-100. MR 1295110 (95k:30037)
3.: W. C. Ma, D. Minda, Hyperbolically convex functions II, Ann. Polon. Math. 71 (1999), no. 3, 273-285. MR 1704303 (2000j:30020)
4.: P. Mattila, Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability, Cambridge University Press (1995). MR 1333890 (96h:28006)
5.: D. Mejia, Chr. Pommerenke, Hyperbolically convex functions, dimension and capacity, Complex Var. Theory Appl. 47 (2002), no. 9, 803-814. MR 1925176 (2003f:30017)
6.: D. Mejia, Chr. Pommerenke, Hyperbolically convex functions, Analysis and applications--ISAAC 2001 (Berlin), 89-95, Int. Soc. Anal. Appl. Comput., 10, Kluwer Acad. Publ., Dordrecht, 2003. MR 2022741 (2004k:30108)
7.: D. Mejia, Chr. Pommerenke, On the derivative of hyperbolically convex functions, Ann. Acad. Sci. Fenn. Math. 27 (2002), no. 1, 47-56. MR 1884348 (2003b:30016)
8.: Chr. Pommerenke, Boundary behaviour of conformal maps, Springer (1992). MR 1217706 (95b:30008)
9.: S. Rohde, On the theorem of Hayman and Wu, Proc. Amer. Math. Soc. 130 (2002), no. 2, 387-394. MR 1862117 (2002i:30010)

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S. Rohde
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195

DOI: 10.1090/S0002-9939-06-08562-5
PII: S 0002-9939(06)08562-5
Received by editor(s): November 9, 2004
Received by editor(s) in revised form: November 16, 2005
Posted: November 13, 2006
Additional Notes: The author was partially supported by NSF Grants DMS-0201435 and DMS-0244408.
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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