Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 339-01. Entropy equality and local symmetry in negative curvature
Manuscript map · lines 8955–8964
OpenAI@2026-10-07#rem:oai-p-339-01
Authors: OpenAI. Family 339.
Title: Entropy equality and local symmetry in negative curvature.
Abstract: For every closed connected smooth Riemannian manifold of dimension at least three with strictly negative sectional curvature, we prove that normalized Liouville measure has maximal entropy for the unit-speed geodesic flow if and only if the metric is locally symmetric. This resolves Katok's entropy rigidity conjecture positively in these dimensions, including all rank-one symmetric types at arbitrary scale.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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