Growth and two-point distortion for biholomorphic mappings of the ball

References

• Blatter , Ch . 1978 . Ein Verzerrungsatz für schlichte Funktionen . Commentarii Mathematici Helvetici , 53 : 651 – 659 .
   Web of Science ®Google Scholar
• Fan , K . 1978 . Distortion of univalent functions . Journal of Mathematical Analysis and Application , 66 : 626 – 631 .
   Web of Science ®Google Scholar
• Kim , SA and Minda , CD . 1994 . Two point distortion theorems for univalent functions . Pacific Journal of Mathematics , 163 : 137 – 157 .
   Web of Science ®Google Scholar
• Ma , W and Minda , CD . 1999 . Two-point distortion for univalent functions . Journal of Computational and Applied Mathematics , 105 : 385 – 392 .
   Web of Science ®Google Scholar
• Kraus , D and Roth , O . 2006 . Weighted distortion in conformal mapping in Euclidean, hyperbolic and elliptic geometry . Annales Academic Fennicae Mathematica , 31 : 111 – 130 .
   Google Scholar
• Pommerenke , Ch . 1964 . Linear-invariante Familien analytischer Funktionen I . Mathematische Annalen , 155 : 108 – 154 .
   Web of Science ®Google Scholar
• Ma , W and Minda , CD . 1997 . Two-point distortion theorems for strongly close-to-convex functions . Complex Variables, Theory and Application , 33 : 185 – 205 .
   Google Scholar
• Hörmander , L . 1954 . On a theorem of Grace . Mathematica Scandinavica , 2 : 55 – 64 .
   Google Scholar
• Harris , LA . 1971 . The numerical range of holomorphic functions in Banach spaces . American Journal of Mathematics , 93 : 1005 – 1019 .
   Web of Science ®Google Scholar
• Bonsall , FF and Duncan , J . 1971 . Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras , London Mathematical Society Lecture Note Series Vol. 2 , Cambridge University Press : Cambridge .
   Google Scholar
• Gustafson , KE and Rao , DKM . 1997 . Numerical Range , New York : Springer-Verlag .
   Google Scholar
• Rudin , W . 1980 . Function Theory in the Unit Ball of , Springer-Verlag : New York .
   Google Scholar
• Pfaltzgraff , JA and Suffridge , TJ . 2000 . Norm order and geometric properties of holomorphic mappings in . Journal d'Analyse Mathématique , 82 : 285 – 313 .
   Web of Science ®Google Scholar
• Pfaltzgraff , JA . 1997 . Distortion of locally biholomorphic maps of the . n -ball. Complex Variables, Theory and Application , 33 : 239 – 253 .
   Google Scholar
• Gong , S . 1998 . Convex and Starlike Mappings in Several Complex Variables , Dordrecht : Kluwer Acad. Publ. .
   Google Scholar
• Jarnicki , M and Pflug , P . 1993 . Invariant Distances and Metrics in Complex Analysis , Berlin-New York : Walter de Gruyter & Co. .
   Google Scholar
• Krantz , SG . 2001 . Function Theory of Several Complex Variables , Providence, R. I : AMS Chelsea Publishing . Reprint of the 1992 edition
   Google Scholar
• Kohr , G . 1999 . On some distortion results for convex mappings in . Complex Variables, Theory and Application , 39 : 161 – 175 .
   Google Scholar
• Graham , I and Kohr , G . 2003 . Geometric Function Theory in One and Higher Dimensions , New York : Marcel Dekker Inc. .
   Google Scholar