Effective formulas for complex geodesics in generalized pseudoellipsoids with applications

Włodzimierz Zwonek

Annales Polonici Mathematici (1995)

  • Volume: 61, Issue: 3, page 261-294
  • ISSN: 0066-2216

Abstract

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We introduce a class of generalized pseudoellipsoids and we get formulas for their complex geodesics in the convex case. Using these formulas we get a description of automorphisms of the pseudoellipsoids. We also solve the problem of biholomorphic equivalence of convex complex ellipsoids without any sophisticated machinery.

How to cite

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Włodzimierz Zwonek. "Effective formulas for complex geodesics in generalized pseudoellipsoids with applications." Annales Polonici Mathematici 61.3 (1995): 261-294. <http://eudml.org/doc/262346>.

@article{WłodzimierzZwonek1995,
abstract = {We introduce a class of generalized pseudoellipsoids and we get formulas for their complex geodesics in the convex case. Using these formulas we get a description of automorphisms of the pseudoellipsoids. We also solve the problem of biholomorphic equivalence of convex complex ellipsoids without any sophisticated machinery.},
author = {Włodzimierz Zwonek},
journal = {Annales Polonici Mathematici},
keywords = {complex geodesics; generalized pseudoellipsoids; biholomorphic equivalence of ellipsoids},
language = {eng},
number = {3},
pages = {261-294},
title = {Effective formulas for complex geodesics in generalized pseudoellipsoids with applications},
url = {http://eudml.org/doc/262346},
volume = {61},
year = {1995},
}

TY - JOUR
AU - Włodzimierz Zwonek
TI - Effective formulas for complex geodesics in generalized pseudoellipsoids with applications
JO - Annales Polonici Mathematici
PY - 1995
VL - 61
IS - 3
SP - 261
EP - 294
AB - We introduce a class of generalized pseudoellipsoids and we get formulas for their complex geodesics in the convex case. Using these formulas we get a description of automorphisms of the pseudoellipsoids. We also solve the problem of biholomorphic equivalence of convex complex ellipsoids without any sophisticated machinery.
LA - eng
KW - complex geodesics; generalized pseudoellipsoids; biholomorphic equivalence of ellipsoids
UR - http://eudml.org/doc/262346
ER -

References

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  3. [D] S. Dineen, The Schwarz Lemma, Clarendon Press, 1989. Zbl0708.46046
  4. [DT] S. Dineen and R. M. Timoney, Complex geodesics on convex domains, in: Progress in Functional Analysis, K. D. Bierstedt, J. Bonet, J. Horváth and M. Maestre (eds.), Elsevier, 1992, 333-365. Zbl0785.46044
  5. [DP] G. Dini and A. S. Primicerio, Localization principle of automorphisms on generalized pseudoellipsoids, preprint. Zbl0943.32006
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  8. [JP] M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, 1993. Zbl0789.32001
  9. [JPZ] M. Jarnicki, P. Pflug and R. Zeinstra, Geodesics for convex complex ellipsoids, Ann. Scuola Norm. Sup. Pisa 20 (1993), 535-543. Zbl0812.32010
  10. [KU] W. Kaup and H. Upmeier, Banach spaces with biholomorphically equivalent unit balls are isomorphic, Proc. Amer. Math. Soc. 58 (1976), 129-133. Zbl0337.32012
  11. [KKM] A. Kodama, S. Krantz and D. Ma, A characterization of generalized complex ellipsoids in ℂ n and related results, Indiana Univ. Math. J. 41 (1992), 173-195. 
  12. [L] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-479. 
  13. [N] T. Naruki, The holomorphic equivalence problem for a class of Reinhardt domains, Publ. RIMS Kyoto Univ. 4 (1968), 527-543. Zbl0199.41101
  14. [P] E. A. Poletskii, The Euler-Lagrange equations for extremal holomorphic mappings of the unit disk, Michigan Math. J. 30 (1983), 317-333. 
  15. [R] W. Rudin, Holomorphic maps that extend to automorphisms of a ball, Proc. Amer. Math. Soc. 81 (1981), 429-432. Zbl0497.32011

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