Proof of the gradient conjecture of R. Thom

• Autores: Adam Parusinski, T. Mostowski, Krzysztof Kurdyka
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 152, Nº 3, 2000, págs. 763-792
• Idioma: inglés
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• Resumen

  • Let x(t) be a trajectory of the gradient of a real analytic function and suppose that x0 is a limit point of x(t). We prove the gradient conjecture of R. Thom which states that the secants of x(t) at x0 have a limit. Actually we show a stronger statement: the radial projection of x(t) from x0 onto the unit sphere has finite length.