A Local-to-Global Principle for Convexity in Metric Spaces

P. Birtea; J.-P. Ortega; T. S. Ratiu

doi:10.5802/jolt.505

P. Birtea; J.-P. Ortega; T. S. Ratiu

Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 445-469

Abstract

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.

Zbl

DOI: 10.5802/jolt.505

Classification: 53C23, 53D20
Keywords: Length metric space, convexity, momentum map

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     author = {P. Birtea and J.-P. Ortega and T. S. Ratiu},
     title = {A {Local-to-Global} {Principle} for {Convexity} in {Metric} {Spaces}},
     journal = {Journal of Lie Theory},
     pages = {445--469},
     year = {2008},
     volume = {18},
     number = {2},
     doi = {10.5802/jolt.505},
     zbl = {1148.53030},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.505/}
}

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P. Birtea; J.-P. Ortega; T. S. Ratiu. A Local-to-Global Principle for Convexity in Metric Spaces. Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 445-469. doi: 10.5802/jolt.505

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