The Cayley hyperbolic space and volume entropy rigidity

MATHEMATISCHE ZEITSCHRIFT(2022)

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摘要
Let $M$ be a Riemannian manifold with dimension greater or equal to $3$ which admits a complete, finite-volume Riemannian metric $g_0$ locally isometric to a rank-1 symmetric space of non-compact type. The volume entropy rigidity theorem 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.
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关键词
Volume growth entropy,The Cayley hyperbolic space,Rigidity,Busemann functions
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