∑math20

Differential geometry · Result 344

The metric Blaschke conjecture

1 paper

Proves the metric Blaschke conjecture: every closed connected Riemannian manifold of positive dimension whose injectivity radius equals its diameter is, up to scaling, a standard compact rank-one symmetric space.

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▶Introduction: the problem and why it mattersin preparation
▶The presented solutionin preparation

Papers 1

First page of The metric Blaschke theorem

The metric Blaschke theorem

OpenAI · September 23, 2026

We prove the metric Blaschke conjecture: every connected closed smooth Riemannian manifold of positive dimension whose global injectivity radius equals its diameter is, up to scale, a standard compact rank-one symmetric space.

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@misc{OAI:The-metric-Blaschke-theorem-September-23-2026,
  author = {{OpenAI}},
  title = {{The metric Blaschke theorem}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-metric-Blaschke-theorem-September-23-2026/paper.pdf}{OAI:The-metric-Blaschke-theorem-September-23-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.