Geodesic
Ravines of functions and nonuniformity of their supergraphs
Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 95-115.

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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. 
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     title = {Ravines of functions and nonuniformity of their supergraphs},
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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/