The metric Blaschke conjecture

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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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The paper states

Theorem 1.1 (The metric Blaschke theorem)

In The metric Blaschke theorem, 23 September 2026

Possible match to OpenAI’s description, selected from the papers’ main statements because it shares the most wording. No review confirming the selection is recorded.

The other possible matches are Theorem 1.2 (Sharp volume comparison) in the same paper () and Corollary 1.3 (Reduction to an upper volume bound) in the same paper ().

Let (M,g) be a connected closed smooth Riemannian manifold of positive dimension. If \inj(M,g)=\diam(M,g), then (M,g) is isometric, up to multiplication of the metric by a positive constant, to a round sphere, a standard real, complex or quaternionic projective space, or the Cayley plane.

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The metric Blaschke theorem

23 September 2026, current edition.

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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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29 references in The metric Blaschke theorem

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