Mumford's compactness theorem
id:
mumford-s-compactness-theorem-314-10229384
title:
Mumford's compactness theorem
text:
In mathematics, Mumford's compactness theorem states that the space of compact Riemann surfaces of fixed genus g > 1 with no closed geodesics of length less than some fixed ε > 0 in the Poincaré metric is compact. It was proved by David Mumford (1971) as a consequence of a theorem about the compactness of sets of discrete subgroups of semisimple Lie groups generalizing Mahler's compactness theorem.
brand slug:
wiki
category slug:
encyclopedia
description:
Gives conditions for a space of compact Riemann surfaces of genus > 1 to be compact
original url:
https://en.wikipedia.org/wiki/Mumford%27s_compactness_theorem
date created:
date modified:
2023-08-12T00:30:15Z
main entity:
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image:
fields total:
13
integrity:
14