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On the behavior of complete graphs in \({\mathbb{R}\sp{n+1}}\) with L p-finite r-curvature

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Abstract

We study the behavior of complete graphs in \({\mathbb{R}\sp{n+1}}\) with L p-finite r-curvature, that is, whose length of the r-th Newton transformation |P r | is in L p, for some p ≥ 1. Moreover, we use a monotonicity formulae to establish an L p-lower bound for |P r | in balls. As application, we prove some new Bernstein-type results.

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  1. Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, Bl. 914, 60455-760, Fortaleza, CE, Brazil

    Cleon S. Barroso

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  1. Cleon S. Barroso
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Barroso, C.S. On the behavior of complete graphs in \({\mathbb{R}\sp{n+1}}\) with L p-finite r-curvature. Ann Glob Anal Geom 35, 231–241 (2009). https://doi.org/10.1007/s10455-008-9132-x

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