OpenAI reports convex tangent injectivity domains under weak MTW
- Mathematics
On every compact connected smooth Riemannian manifold of dimension at least two satisfying weak Ma–Trudinger–Wang curvature, each open tangent injectivity domain is convex.
OpenAI reports convex tangent injectivity domains under weak MTW
- Mathematics
On every compact connected smooth Riemannian manifold of dimension at least two satisfying weak Ma–Trudinger–Wang curvature, each open tangent injectivity domain is convex.
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Understand the problem ↓Understanding the problem
Read the background
On every compact connected smooth Riemannian manifold of dimension at least two satisfying weak Ma–Trudinger–Wang curvature, each open tangent injectivity domain is convex.
Why it matters
If correct, resolves Villani’s injectivity-domain convexity conjecture in the compact setting without nonfocality.
What counts as progress
Does weak MTW curvature force convex tangent injectivity domains?
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OpenAI reports convex tangent injectivity domains under weak MTW