Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 360-01. Global Support and Convex Injectivity Domains under Weak MTW
Manuscript map · lines 9305–9314
OpenAI@2026-10-07#rem:oai-p-360-01
Authors: OpenAI. Family 360.
Title: Global Support and Convex Injectivity Domains under Weak MTW.
Abstract: We prove that weak Ma–Trudinger–Wang curvature on a smooth, connected, compact Riemannian manifold of dimension at least two without boundary implies convexity of every tangent injectivity domain, resolving Villani's conjecture in this setting. Conjugate cut points are allowed. More generally, every ordinary subgradient of a squared-distance cost potential is a minimizing velocity with a global supporting mountain. No density hypothesis is used.
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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