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.
Citation
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
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