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A refinement of the complex convexity theorem via symplectic techniques
Author(s):
Bernhard
Krötz;
Michael
Otto
Journal:
Proc. Amer. Math. Soc.
134
(2006),
549-558.
MSC (2000):
Primary 53D20, 22E15
Posted:
June 14, 2005
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Abstract:
We apply techniques from symplectic geometry to extend and give a new proof of the complex convexity theorem of Gindikin-Krötz.
References:
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- 1.
- Akhiezer, D., and S. Gindikin, On Stein extensions of real symmetric spaces, Math. Ann. 286 (1990), 1-12. MR 1032920 (91a:32047)
- 2.
- Atiyah, M.F, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1) (1982), 1-15. MR 0642416 (83e:53037)
- 3.
- Duistermaat, J.J., Convexity and tightness for restrictions of Hamiltonian functions to fixed point sets of an antisymplectic involution, Trans. Amer. Math. Soc. 275 (1983), no. 1, 417-429. MR 0678361 (84c:53035)
- 4.
- De Concini, C., and C. Procesi, Quantum groups, Springer LNM 1565 (1992), 31-140. MR 1288995 (95j:17012)
- 5.
- Gindikin, S., and B. Krötz, Invariant Stein domains in Stein symmetric spaces and a non-linear complex convexity theorem, IMRN 18 (2002), 959-971. MR 1902298 (2003d:32026)
- 6.
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- 7.
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- 8.
- Krötz, B., and M. Otto, Lagrangian submanifolds and moment convexity, Trans. Amer. Math. Soc., to appear.
- 9.
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Additional Information:
Bernhard
Krötz
Affiliation:
Department of Mathematics, MS 1222, University of Oregon, Eugene, Oregon 97403-1222
Address at time of publication:
Max-Planck Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany
Email:
kroetz@math.iisc.ernet.in
Michael
Otto
Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210-1174
Address at time of publication:
Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, P.O. Box 210089, Tucson, Arizona 85721-0089
Email:
otto@math.arizona.edu
DOI:
10.1090/S0002-9939-05-08079-2
PII:
S 0002-9939(05)08079-2
Received by editor(s):
January 22, 2004
Received by editor(s) in revised form:
September 14, 2004
Posted:
June 14, 2005
Additional Notes:
The first author was supported in part by NSF grant DMS-0097314
Communicated by:
Dan M. Barbasch
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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