From:  (Schramm Oded)
Newsgroups:     sci.math.research
Subject:        2 convex curves intersecting in 3 or more points
Date:           Mon, 18 Sep 1995 12:01:12 GMT
Organization:   Weizmann Institute of Science
Summary:        their curvatures are related
Keywords:       curvature

Lemma:  Let g, h be two convex planar curves (sufficiently differentiable
so that the curvature is defined), which share at least 3 points. 
Then min k_g < max k_h; that is, the minimum of the curvature of g
is at most the maximum of the curvature of h.

It is likely that this result is known.  If you recognize it, please 
inform me.

I have an elementary proof, and two nice applications,
related to conformal maps.

Oded Schramm  

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