Journal of Lie Theory 18 (2008), No. 2, 445--469
Copyright Heldermann Verlag 2008
A Local-to-Global Principle for Convexity in Metric Spaces
Petre Birtea
Departamentul de Matematica, Universitatea de Vest, 1900 Timisoara, Romania
birtea@math.uvt.ro
Juan-Pablo Ortega
CNRS - Dép. de Mathématiques, Université de Franche-Comté, UFR des Sciences et Techniques, 16 route de Gray, 25030 Besancon, France
Juan-Pablo.Ortega@univ-fcomte.fr
Tudor S. Ratiu
Section de Mathématiques and Bernoulli Center, Ècole Polytechnique Fédérale, 1015 Lausanne, Switzerland
tudor.ratiu@epfl.ch
We introduce an extension of the standard Local-to-Global Principle used in the proof of the convexity theorems for the momentum map to handle closed maps that take values in a length metric space. As an application, this extension is used to study the convexity properties of the cylinder valued momentum map introduced by Condevaux, Dazord, and Molino.
Keywords: Length metric space, convexity, momentum map.
MSC: 53C23, 53D20
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