Łojasiewicz exponents of non-degenerate holomorohic and mixed functions

Abstract

We consider Łojasiewicz inequalities for a non-degenerate holomorphic function with an isolated singularity at the origin. We give an explicit estimation of the Łojasiewicz exponent in a slightly weaker form than the assertion in Fukui.For a weighted homogeneous polynomial, we give a better estimation in the form which is conjectured by Brzostowski, Krasinski and Oleksik under under some condition (the Łojasiewicz non-degeneracy). We also introduce Łojasiewicz inequality for strongly non-degenerate mixed functions and generalize this estimation for mixed functions.

33 pages

Cited by in corpus (2)

• Łojasiewicz exponents of a certain analytic functions
• The Łojasiewicz exponent of non-degenerate surface singularities