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- Title
The Cayley hyperbolic space and volume entropy rigidity.
- Authors
Ruan, Yuping
- Abstract
Let M be a Riemannian manifold with dimension greater than or equal to 3 which admits a complete, finite-volume Riemannian metric g 0 locally isometric to a rank one symmetric space of non-compact type. The volume entropy rigidity theorem (Besson et al. in Geom Funct Anal 5(5), 731–799, 1995, Theorémè principal) asserts that g 0 minimizes a normalized volume growth entropy among all complete, finite-volume, Riemannian metric on M. We will repair a gap in the proof when g 0 is locally isometric to the Cayley hyperbolic space.
- Subjects
HYPERBOLIC spaces; RIEMANNIAN metric; SYMMETRIC spaces; ENTROPY; GEOMETRIC rigidity; CAYLEY graphs
- Publication
Mathematische Zeitschrift, 2024, Vol 306, Issue 1, p1
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-023-03398-0