Preprint version. Published in Indiana University Mathematics, Volume 42, Issue 1, January 1, 1993, pages 37-53.
NOTE: At the time of publication, the author Joseph E. Borzellino was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1512/iumj.1993.42.42004.
In this paper the Maximal Diameter Theorem of Riemannian geometry is proven for Riemannian orbifolds. In particular, it is shown that a complete Riemannian orbifold with Ricci curvature bounded below by (n−1) and diameter = π, must have constant sectional curvature 1, and must be a quotient of the sphere (Sn, can) of constant sectional curvature 1 by a subgroup of the orthogonal group O(n+1) acting discontinuously and isometrically on Sn. It is also shown that the singular locus of the orbifold forms a geometric barrier to the length minimization property of geodesics. We also extend the Bishop relative volume comparison theorem to Riemannian orbifolds.