https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Comparison_theorem 2026-05-28T16:42:46Z Revision history for this page on the wiki MediaWiki 1.41.2 https://diffgeom.subwiki.org/w/index.php?title=Comparison_theorem&diff=160&oldid=prev 2008-05-18T19:34:48Z

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Vipul https://diffgeom.subwiki.org/w/index.php?title=Comparison_theorem&diff=159&oldid=prev 2007-04-09T06:25:23Z

<p></p> <p><b>New page</b></p><div>{{survey article}}<br /> <br /> {{particularcases|[[:Category: Comparison theorems]]}}<br /> <br /> ==Description==<br /> <br /> A &#039;&#039;&#039;comparison theorem&#039;&#039;&#039; is a result that relates, or compares, properties and quantities associated with a given Riemannian manifold, to properties and quantities associated with a Riemannian manifold equipped with a [[constant-curvature metric]], viz a metric of constant sectional curvature.<br /> <br /> The &#039;&#039;model&#039;&#039; Riemannian manifold (the one with constant-curvature) is typically taken to be a Riemannian manifold whose constant curvature is a bound on the sectional curvature (or Ricci curvature) of the given Riemannian manifold.</div>

Vipul