The Boundary Conjecture for Leaf Spaces

2018/04/05 by Grove, Karsten, Moreno, Adam, Petersen, Peter
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1804.01656

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.

Cited by

• Transverse sphere theorems for Riemannian foliations

Related

• Rigidity for positively curved Alexandrov spaces with boundary
• Isometries between leaf spaces
• Bounded geometry and leaves
• Sharp bounds and rigidity for volumes of boundaries of Alexandrov spaces
• On the Structure of Equidistant Foliations of Euclidean Space