Teissier, Bernard; Matematični kolokvij november 2013

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Some recent developments around the Łojasiewicz inequality

Bernard Teissier

Institut de Mathématiques de Jussieu, Paris

14. november 2013


The Łojasiewicz inequality states that if a real (sub)analytic function f on an open set U of {\mathbf R}^n vanishes on the zero set of another (sub)analytic function g, then there is a reason: for every compact subset K of U, there exist C > 0 and θ > 0 such that on K we have \vert f\vert <c\vert g\vert ^\theta. This has had many resonances in analysis, algebra, algebraic geometry. I will describe some of them, as well as some properties of the best possible exponent θ and its relation with the geometry of the map (f,g)\colon U\to \mathbf R^2.


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