From:schramm@nufar.wisdom.weizmann.ac.il (Schramm Oded)Newsgroups:sci.math.researchSubject:2 convex curves intersecting in 3 or more pointsDate:Mon, 18 Sep 1995 12:01:12 GMTOrganization:Weizmann Institute of ScienceSummary:their curvatures are relatedKeywords: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 schramm@wisdom.weizmann.ac.il %! PostScript 300 425 translate /d {exch def} def 1 1 .95 /h d 15 /r d { 0 0 r 0 360 arc stroke}/c d{exch 1 exch div 1 h div /h d}/i d{1 index 1 atan 2 mul rotate} /t d{dup r mul dup r exch translate /r d -90 rotate exch h mul exch t c}/k d {k i t n {k} repeat} /z d c 0 /n d 20 {z n 1 add /n d z} repeat showpage