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arXiv · 2311.03298

Lojasiewicz inequalities in a certain class of smooth functions

Ha Minh Lam·Ha Huy Vui
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Abstract

Let $f$ be a germ of a smooth function at the orirgin in $\RR^n.$ We show that if $f$ is Kouchnirenko's nondegenerate and satisfies the so called Kamimoto--Nose condition then it admits the \L ojasiewicz inequalities. We compute the \L ojasiewicz exponents for some special cases. In particular, if $f$ is a germ of a smooth convex Kouchnirenko's nondegenerate function and satisfies the Kamimoto--Nose condition, then all its \L ojasiewicz exponents can be expressed very simply in terms of its Newton polyhedron.

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Ha Minh Lam, Ha Huy Vui. 2023-11-06. Lojasiewicz inequalities in a certain class of smooth functions. https://arxiv.org/abs/2311.03298

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