English

The Cayley hyperbolic space and volume entropy rigidity

Differential Geometry 2022-03-29 v1

Abstract

Let MM be a Riemannian manifold with dimension greater or equal to 33 which admits a complete, finite-volume Riemannian metric g0g_0 locally isometric to a rank-1 symmetric space of non-compact type. The volume entropy rigidity theorem asserts that g0g_0 minimizes a normalized volume growth entropy among all complete, finite-volume, Riemannian metric on MM. We will repair a gap in the proof when g0g_0 is locally isometric to the Cayley hyperbolic space.

Keywords

Cite

@article{arxiv.2203.14418,
  title  = {The Cayley hyperbolic space and volume entropy rigidity},
  author = {Yuping Ruan},
  journal= {arXiv preprint arXiv:2203.14418},
  year   = {2022}
}
R2 v1 2026-06-24T10:27:40.425Z