Geodesic
Ravines of functions and nonuniformity of their supergraphs
Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 95-115 
E. G. Belousov; E. G. Andronov. Ravines of functions and nonuniformity of their supergraphs. Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 95-115. http://geodesic.mathdoc.fr/item/DM_1995_7_4_a8/
@article{DM_1995_7_4_a8,
     author = {E. G. Belousov and E. G. Andronov},
     title = {Ravines of functions and nonuniformity of their supergraphs},
     journal = {Diskretnaya Matematika},
     pages = {95--115},
     year = {1995},
     volume = {7},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1995_7_4_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce the notion of an $L$-ravine of a function, which is a generalization of the notion of a $c$-ravine introduced in [1], and give examples of functions, including convex polynomials, with different structures of $L$-ravines.A connection of this notion with non-uniformity of the distribution of integer points, or generally of lattice nodes, in epigraphs of functions is demonstrated. In particular, it is proved that there exist absolutely non-uniform convex polynomials and convex functions in two variables which have no $c$-ravines but have $L$-ravines.