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The diameter sphere theorem up to diffeomorphism
Decide whether a manifold with sectional curvature at least 1 and diameter above π/2 must be diffeomorphic to the standard sphere.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "geometry-topology" | |
| 5 | + ], | |
| 6 | + "type": "proof", | |
| 7 | + "source": { | |
| 8 | + "key": "aimpl", | |
| 9 | + "name": "AIM Problem Lists", | |
| 10 | + "url": "http://aimpl.org/nnsectcurvature/1/", | |
| 11 | + "id": "nnsectcurvature 1.2", | |
| 12 | + "curator": "American Institute of Mathematics", | |
| 13 | + "status": "open", | |
| 14 | + "as_of": "2026-10-20", | |
| 15 | + "catalog": "0521c19bbd38" | |
| 16 | + } | |
| 17 | +} | |