The first diameter of 3-manifolds of positive scalar curvature

Katz, Mikhail

doi:10.1090/S0002-9939-1988-0962834-9

The first diameter of $3$-manifolds of positive scalar curvature
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by Mikhail Katz PDF

Proc. Amer. Math. Soc. 104 (1988), 591-595 Request permission

Abstract:

We seek a universal upper bound for the first diameter of $3$-manifolds of scalar curvature $\geq + 1$. We find it in the case of finite fundamental group by using a combinatorial theorem about finite trees, and in the case when ${\pi _1}$ is infinite cyclic by using a weak notion of a ${\pi _1}$-equivariant Busemann function.

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