Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 360-02. Uniform Bi-Holder Transport from Weak MTW
Manuscript map · lines 9315–9324
OpenAI@2026-10-07#rem:oai-p-360-02
Authors: OpenAI. Family 360.
Title: Uniform Bi-Holder Transport from Weak MTW.
Abstract: We prove that the weak Ma–Trudinger–Wang condition on a fixed smooth connected compact boundaryless Riemannian manifold of dimension at least two implies a common Hölder estimate for optimal transport maps and their inverses over the entire class of probability densities with fixed positive upper and lower bounds. The maps have homeomorphic representatives, conjugate cut points are allowed, and no density regularity is assumed.
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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