A Sturm-type comparison theorem by a geometric study of plane multihedgehogs
Yves Martinez-Maure
Source: Illinois J. Math. Volume 52, Number 3
(2008), 981-993.
Abstract
We prove a Sturm-type comparison theorem by a geometric study of plane (multi)hedgehogs. This theorem implies that for every 2π-periodic smooth real function h, the number of zeros of h in [0, 2π[ is not bigger than the number of zeros of h+h′′ 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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Permanent link to this document: http://projecteuclid.org/euclid.ijm/1254403726
Zentralblatt MATH identifier: 05615680
Mathematical Reviews number (MathSciNet): MR2546019
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Illinois Journal of Mathematics
