Let M be a connected symplectic manifold on which a torus T acts in a Hamiltonian fashion and denote by f the corresponding moment map. If M is compact, the Atiyah, Guillemin- Sternberg theorem says that the set f(M) is convex; if M is noncompact this may not be the case. We show that if M is suitably convex, then f(M) can be explicitly described as the convex hull of a finite number of affine rays. As an application, we obtain a natural symplectic proof of the Paneitz convexity theorem for the positive Kaehler elliptic co-adjoint orbits.

Convexity properties of the moment map for certain non-compact manifolds / E. Prato. - In: COMMUNICATIONS IN ANALYSIS AND GEOMETRY. - ISSN 1019-8385. - STAMPA. - 2:(1994), pp. 267-278. [10.4310/CAG.1994.V2.N2.A5]

Convexity properties of the moment map for certain non-compact manifolds

PRATO, ELISA
1994

Abstract

Let M be a connected symplectic manifold on which a torus T acts in a Hamiltonian fashion and denote by f the corresponding moment map. If M is compact, the Atiyah, Guillemin- Sternberg theorem says that the set f(M) is convex; if M is noncompact this may not be the case. We show that if M is suitably convex, then f(M) can be explicitly described as the convex hull of a finite number of affine rays. As an application, we obtain a natural symplectic proof of the Paneitz convexity theorem for the positive Kaehler elliptic co-adjoint orbits.
1994
2
267
278
E. Prato
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/255432
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