Theorems in analysis

Gradient conjecture

In mathematics, the gradient conjecture, due to René Thom (1989), was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka (University of Savoie, France), Tadeusz Mostowski (Warsaw University, Poland) and Adam Parusiński (University of Angers, France). The conjecture states that given a real-valued analytic function f defined on Rn and a trajectory x(t) of the gradient vector field of f having a limit point x0 ∈ Rn, where f has an isolated critical point at x0, there exists a limit (in the projective space PRn-1) for the secant lines from x(t) to x0, as t tends to zero. The proof depends on a theorem due to Stanisław Łojasiewicz. (Wikipedia).

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From playlist Engineering Mathematics

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From playlist Calculus 3

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From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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Related pages

Projective space | Secant line | Analytic function | Mathematics | Gradient