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Fall 2008 A Sturm-type comparison theorem by a geometric study of plane multihedgehogs
Yves Martinez-Maure
Illinois J. Math. 52(3): 981-993 (Fall 2008). DOI: 10.1215/ijm/1254403726

Abstract

We prove a Sturm-type comparison theorem by a geometric study of plane (multi)hedgehogs. This theorem implies that for every $2\pi$-periodic smooth real function $h$, the number of zeros of $h$ in $[0,2\pi[$ is not bigger than the number of zeros of $h+h^{\prime\prime}$ plus $2$. In terms of $N$-hedgehogs, it can be interpreted as a comparison theorem between number of singularities and maximal number of support lines through a point. The rest of the paper is devoted to a series of geometric consequences.

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Yves Martinez-Maure. "A Sturm-type comparison theorem by a geometric study of plane multihedgehogs." Illinois J. Math. 52 (3) 981 - 993, Fall 2008. https://doi.org/10.1215/ijm/1254403726

Information

Published: Fall 2008
First available in Project Euclid: 1 October 2009

zbMATH: 1202.26019
MathSciNet: MR2546019
Digital Object Identifier: 10.1215/ijm/1254403726

Subjects:
Primary: 52A30, 53A04

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 3 • Fall 2008
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