Independent Bonnet--Myers diameter and compactness theorem

Arthur Freitas Ramos, David Barros Hulak, Ruy J. G. B. de Queiroz

Palomar Registrypalomar/PALOMAR-2026-09-11-000001Sep 11, 2026math.DGscore 0

Formalizes the classical Bonnet--Myers theorem for complete connected smooth boundaryless finite-dimensional real Riemannian manifolds. From dimension n >= 2, K > 0, and the pointwise lower bound Ric(a,a) >= (n-1) K g(a,a), the selected theorem constructs the Levi--Civita connection and actual curvature, proves compactness, and gives the sharp induced extended-diameter bound pi/sqrt K. The development proves minimizing-geodesic, parallel-transport, second-variation, index-form, and metric-compactness bridges rather than assuming them.

SourceRepositoryJSON

Comments and reviews

No comments yet.

API

curl /api/v1/records/palomar/PALOMAR-2026-09-11-000001
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-11-000001/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-11-000001/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'