Geodesic
Extremal property of some surfaces in $n$-dimensional Euclidean space
Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 247-254 
V. I. Bernik; É. I. Kovalevskaya. Extremal property of some surfaces in $n$-dimensional Euclidean space. Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 247-254. http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a9/
@article{MZM_1974_15_2_a9,
     author = {V. I. Bernik and \'E. I. Kovalevskaya},
     title = {Extremal property of some surfaces in $n$-dimensional {Euclidean} space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {247--254},
     year = {1974},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A surface $\Gamma(f_1(x_1,\dots,x_m),\dots,f_n(x_1,\dots,x_n))$ is said to be extremal if for almost all points of $\Gamma$ the inequality $$\|\alpha_1f_1(x_1,\dots,x_m)+\dots+\alpha_nf_n(x_1,\dots,x_n)\|<H^{-n-\varepsilon},$$ where $H=\max(|\alpha_i|)$, ($i=1,2,\dots,n$), has only a finite number of solutions in the integers $\alpha_1,\dots,\alpha_n$. In this note we prove, for a specific relationship between $m$ and $n$ and a functional condition on the functions $f_1,\dots,f_n$, the extremality of a class of surfaces in $n$-dimensional Euclidean space.