The Boundary Conjecture for Leaf Spaces
Differential Geometry
2018-04-06 v1 Metric Geometry
Abstract
We prove that the boundary of an orbit space or more generally a leaf space of a singular Riemannian foliation is an Alexandrov space in its intrinsic metric, and that its lower curvature bound is that of the leaf space. A rigidity theorem for positively curved leaf spaces with maximal boundary volume is also established and plays a key role in the proof of the boundary problem.
Cite
@article{arxiv.1804.01656,
title = {The Boundary Conjecture for Leaf Spaces},
author = {Karsten Grove and Adam Moreno and Peter Petersen},
journal= {arXiv preprint arXiv:1804.01656},
year = {2018}
}
Comments
7 pages