Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Invariant holomorphic discs in some non-convex domains

Authors: Florian Bertrand and Hervé Gaussier
Journal: Proc. Amer. Math. Soc. 146 (2018), 1197-1205
MSC (2010): Primary 32F45, 32Q45
Published electronically: October 6, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a description of complex geodesics and we study the structure of stationary discs in some non-convex domains for which complex geodesics are not unique.

References [Enhancements On Off] (What's this?)

  • [1] Marco Abate, Iteration theory of holomorphic maps on taut manifolds, Research and Lecture Notes in Mathematics. Complex Analysis and Geometry, Mediterranean Press, Rende, 1989. MR 1098711
  • [2] Josip Globevnik, Perturbing analytic discs attached to maximal real submanifolds of $ {\bf C}^N$, Indag. Math. (N.S.) 7 (1996), no. 1, 37-46. MR 1621348,
  • [3] Shoshichi Kobayashi, Hyperbolic complex spaces, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 318, Springer-Verlag, Berlin, 1998. MR 1635983
  • [4] László Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), no. 4, 427-474 (French, with English summary). MR 660145
  • [5] Myung-Yull Pang, Smoothness of the Kobayashi metric of nonconvex domains, Internat. J. Math. 4 (1993), no. 6, 953-987. MR 1250257,
  • [6] Halsey Royden, Pit-Mann Wong, and Steven G. Krantz, The Carathéodory and Kobayashi/Royden metrics by way of dual extremal problems, Complex Var. Elliptic Equ. 58 (2013), no. 9, 1283-1298. MR 3170699,
  • [7] N. Sibony, Remarks on the Kobayashi metric, unpublished note.
  • [8] A. Tumanov, Extremal discs and the regularity of CR mappings in higher codimension, Amer. J. Math. 123 (2001), no. 3, 445-473. MR 1833148
  • [9] N. P. Vekua, Systems of singular integral equations, translated from the Russian by A. G. Gibbs and G. M. Simmons, edited by J. H. Ferziger, P. Noordhoff, Ltd., Groningen, 1967. MR 0211220
  • [10] Edoardo Vesentini, Complex geodesics, Compositio Math. 44 (1981), no. 1-3, 375-394. MR 662466

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 32F45, 32Q45

Retrieve articles in all journals with MSC (2010): 32F45, 32Q45

Additional Information

Florian Bertrand
Affiliation: Department of Mathematics, American University of Beirut, Beirut, Lebanon

Hervé Gaussier
Affiliation: Université Grenoble Alpes, CNRS, IF, F-38000 Grenoble, France

Keywords: Kobayashi metric, extremal disc, complex geodesic, stationary disc
Received by editor(s): April 10, 2017
Received by editor(s) in revised form: May 2, 2017
Published electronically: October 6, 2017
Additional Notes: The research of the two authors was partially supported by the CEDRE Grant 35398TK
Communicated by: Filippo Bracci
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society