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Orbifolds of maximal diameter. (English) Zbl 0801.53031
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 $$= \pi$$, must have constant sectional curvature 1, and must be a quotient of the sphere ($$S^ n$$,can) of constant sectional curvature 1 by a subgroup of the orthogonal group $$\mathbb{O}(n+1)$$ acting discontinuously and isometrically on $$S^ n$$. 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.

##### MSC:
 53C20 Global Riemannian geometry, including pinching
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