Geodesic
Curvature extrema and four-vertex-theorems for polygons and polyhedra
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 251-271 Cet article a éte moissonné depuis la source Math-Net.Ru

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Discrete analogs of curvature etrema and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. Several interrelated approaches are considered. One of the main results says that a regular triangulation of a $d$-ball containing $\ge d$ simplices has at least $d$ “ears”. 
@article{ZNSL_2001_280_a18,
     author = {O. R. Musin},
     title = {Curvature extrema and four-vertex-theorems for polygons and polyhedra},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {251--271},
     year = {2001},
     volume = {280},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a18/}
}
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O. R. Musin. Curvature extrema and four-vertex-theorems for polygons and polyhedra. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 251-271. http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a18/