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The first diameter of $ 3$-manifolds of positive scalar curvature


Author: Mikhail Katz
Journal: Proc. Amer. Math. Soc. 104 (1988), 591-595
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1988-0962834-9
MathSciNet review: 962834
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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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DOI: https://doi.org/10.1090/S0002-9939-1988-0962834-9
Article copyright: © Copyright 1988 American Mathematical Society

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