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Proof of the gradient conjecture of R. Thom

Krzysztof Kurdyka·Tadeusz Mostowski·Adam Parusinski
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Abstract

Let x(t) be a trajectory of the gradient of a real analytic function and suppose that x_0 is a limit point of x(t). We prove the gradient conjecture of R. Thom which states that the secants of x(t) at x_0 have a limit. Actually we show a stronger statement: the radial projection of x(t) from x_0 onto the unit sphere has finite length.

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Krzysztof Kurdyka, Tadeusz Mostowski, Adam Parusinski. 2000-11-01. Proof of the gradient conjecture of R. Thom. https://arxiv.org/abs/math/9906212

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