Lagrangian submanifolds and moment convexity

Authors:
Bernhard Krötz and Michael Otto

Journal:
Trans. Amer. Math. Soc. **358** (2006), 799-818

MSC (2000):
Primary 53D20, 22E15

Published electronically:
May 10, 2005

MathSciNet review:
2177041

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a Hamiltonian torus action on a compact connected symplectic manifold and its associated momentum map . For certain Lagrangian submanifolds we show that is convex. The submanifolds arise as the fixed point set of an involutive diffeomorphism which satisfies several compatibility conditions with the torus action, but which is in general not anti-symplectic. As an application we complete a symplectic proof of Kostant's non-linear convexity theorem.

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Additional Information

**Bernhard Krötz**

Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1221

Email:
kroetz@math.uoregon.edu

**Michael Otto**

Affiliation:
Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, Ohio

Email:
otto@math.ohio-state.edu

DOI:
https://doi.org/10.1090/S0002-9947-05-03723-2

Received by editor(s):
November 11, 2003

Received by editor(s) in revised form:
March 31, 2004

Published electronically:
May 10, 2005

Additional Notes:
The work of the first author was supported in part by NSF grant DMS-0097314

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.