A Sturm-type comparison theorem by a geometric study of plane multihedgehogs
Martinez-Maure, Yves
Illinois J. Math., Tome 52 (2008) no. 1, p. 981-993 / Harvested from Project Euclid
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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.
Publié le : 2008-05-15
Classification:  52A30,  53A04 
@article{1254403726,
     author = {Martinez-Maure, Yves},
     title = {A Sturm-type comparison theorem by a geometric study of plane multihedgehogs},
     journal = {Illinois J. Math.},
     volume = {52},
     number = {1},
     year = {2008},
     pages = { 981-993},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1254403726}
}

Martinez-Maure, Yves. A Sturm-type comparison theorem by a geometric study of plane multihedgehogs. Illinois J. Math., Tome 52 (2008) no. 1, pp.  981-993. http://gdmltest.u-ga.fr/item/1254403726/