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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.

Keywords

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

R2 v1 2026-06-23T01:14:22.498Z