A rigidity condition for generators in strongly convex domains

References

• Abate , M . 1989 . Iteration Theory of Holomorphic Maps on Taut Manifolds , Rende, Cosenza : Mediterranean Press .
   Google Scholar
• Reich , S and Shoikhet , D . 2005 . Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach spaces , London : Imperial College Press .
   Google Scholar
• Shoikhet , D . 2001 . Semigroups in Geometrical Function Theory , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Berkson , E and Porta , H . 1978 . Semigroups of analytic functions and compositions operators . Michigan Math. J. , 25 : 101 – 115 .
   Google Scholar
• Burns , DM and Krantz , SG . 1994 . Rigidity of holomorphic mapping and a new Scwartz lemma at the boundary . J. Amer. Math. Soc. , 7 ( 3 ) : 661 – 676 .
   Google Scholar
• Tauraso , R and Vlacci , F . 2001 . Rigidity at the boundary for holomorphic self-maps of the unit disc . Complex Var. Theory Appl. , 45 ( 2 ) : 151 – 165 .
   Google Scholar
• Bracci , F , Tauraso , R and Vlacci , F . 2002 . Identity principles for commuting holomorphic self-maps of the unit disc . J. Math. Anal. Appl. , 2 ( 270 ) : 451 – 473 .
   Google Scholar
• Baracco , L , Zaitsev , D and Zampieri , G . 2006 . A Burns–Krantz type theorem for domains with corners . Math. Ann. , 336 ( 3 ) : 491 – 504 .
   Google Scholar
• Huang , XJ . 1995 . A boundary rigidity problem for holomorphic mappings on some weakly pseu doconvex domains . Canad. J. Math. , 47 ( 2 ) : 405 – 420 .
   Google Scholar
• Migliorini , S and Vlacci , F . 2002 . A new rigidity result for holomorphic maps . Indag. Math. (N.S.) ,
   Google Scholar
• Korányi , A and Stein , EM . 1968 . Fatou's theorem for generalized halfplanes . Ann. Scuola Norm. Sup. Pisa , 3 ( 22 ) : 107 – 112 .
   Google Scholar
• Korányi , A . 1969 . Harmonic functions on Hermitian hyperbolic space . Trans. Amer. Math. Soc , : 507 – 516 .
   Google Scholar
• Elin , M , Levenshtein , M , Reich , S and Shoikhet , D . 2008 . A rigidity theorem for holomorphic generators on the Hilbert ball . Proc. Amer. Math. Soc , : 4313 – 4320 .
   Google Scholar
• Elin , M , Levenshtein , M , Reich , S and Shoikhet , D . 2008 . Two rigidity theorems for holomorphic generators of continuous semigroups . J. Non-linear Convex Anal. , : 59 – 64 .
   Google Scholar
• Levenshtein , M , Reich , S and Shoikhet , D . 2007 . An application of the resolvent method to rigidity theory for holomorphic mappings . J. Nonlinear Convex Anal. , : 99 – 103 .
   Google Scholar
• Abate , M . 1990 . The Lindelöf principle and the angular derivative in strongly convex domains . J. Anal. Math. , 54 : 189 – 228 .
   Google Scholar
• Abate , M . 1988 . Horospheres and iterates of holomorphic maps . Math. Z , 198 ( 2 ) : 225 – 238 .
   Google Scholar
• M. Abate, Angular derivatives in several complex variables, in Real Methods in Complex and cr Geometry, D. Zaitsev and G. Zampieri, eds., Springer, Berlin, 2004, pp. 1–47.
   Google Scholar
• Rudin , W . 1980 . Function Theory in the Unit Ball of ℂⁿ , New York, Berlin : Springer-Verlag .
   Google Scholar
• Huang , X . 1994 . A non-degeneracy property of extremal mappings and iterates of holomorphic self-mappings . Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , 21 ( 3 ) : 399 – 419 .
   Google Scholar
• Bracci , F , Contreras , MD and Diaz-Madrigal , S . 2010 . Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains . J. Eur. Math. Soc. , 12 ( 1 ) : 23 – 53 .
   Google Scholar
• Kobayashi , S . 1998 . Hyperbolic Complex Spaces, Grundlehren der Mathematischen Wissenschaften , Vol. 318 , Berlin : Springer-Verlag .
   Google Scholar
• Jarnicki , M and Pflug , P . 1993 . Invariant Distances and Metrics in Complex Analysis, de Gruyter Expositions in Mathematics , Vol. 9 , Berlin : Walter de Gruyter & Co. .
   Google Scholar
• Lempert , L . 1981 . La métrique de kobayashi et la représentation des domaines sur la boule . Bull. Soc. Math. France , 109 ( 4 ) : 427 – 474 .
   Web of Science ®Google Scholar
• Lempert , L . 1984 . Intrinsic distances and holomorphic retracts . Complex Anal. and Appl. , 81 (varna, 1981) : 341 – 364 .
   Google Scholar
• S. Trapani, Dual maps and kobayashi distance of bounded convex domains in ℂn, contemporary geometry and related topics, in Proceedings of the Workshop held in Belgrade, 15–21 May, 2002, 2004, pp. 389–406.
   Google Scholar
• Bracci , F , Patrizo , G and Trapani , S . 2009 . The pluricomplex Poisson kernel for strongly convex domains . Trans. Amer. Math. Soc. , 361 ( 2 ) : 979 – 1005 .
   Google Scholar
• Bracci , F and Patrizio , G . 2005 . Monge–Ampére foliations with singularities at the boundary of strongly convex domains . Math. Ann. , 332 ( 3 ) : 499 – 522 .
   Google Scholar
• Abate , M . 1992 . The infinitesimal generators of semigroups of holomorphic maps . Ann. Mat. Pura Appl. , 161 : 167 – 180 .
   Google Scholar