Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 337-01. Generalized Cartan–Hadamard isoperimetry and Euclidean equality rigidity
Manuscript map · lines 8925–8934
OpenAI@2026-10-07#rem:oai-p-337-01
Authors: OpenAI. Family 337.
Title: Generalized Cartan–Hadamard isoperimetry and Euclidean equality rigidity.
Abstract: We resolve the generalized Cartan–Hadamard isoperimetric conjecture in every dimension. In a complete simply connected smooth manifold with sectional curvature at most κ ≤ 0, every finite-volume set of finite ambient perimeter has perimeter at least that of the equal-volume ball in curvature κ. For bounded positive-volume sets, equality in the Euclidean comparison holds precisely when the set agrees up to null sets with an open region isometric, with its induced metric, to a round Euclidean ball.
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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