A Local-to-Global Principle for Convexity in Metric Spaces
Petre Birtea, Juan‐Pablo Ortega, Tudor Stefan Ratiu · Journal of Lie Theory · 2008
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.