The Boundary Conjecture for Leaf Spaces
Annales de l'Institut Fourier, to appear, 10 p.

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.

On montre que le bord d’un espace d’orbites, ou plus généralement l’espace quotient d’un feuilletage riemannien singulier, est un espace d’Alexandrov muni de sa distance intrinsèque, et que la borne inférieure de sa courbure coincide avec celle de l’espace des feuilles. On établit aussi un théorème de rigidité pour les espaces de feuilles de courbure strictement positive maximisant le volume de leur bord, qui joue un rôle clef dans la preuve du théorème du bord.

Classification: 53C23,  53C12,  53C24,  51K10
Keywords: Alexandrov Geometry, Singular Riemannian Foliations, Leaf Spaces, Lens Charaterization
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Grove, Karsten; Moreno, Adam; Petersen, Peter. The Boundary Conjecture for Leaf Spaces. Annales de l'Institut Fourier, to appear, 10 p.

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