Proof of the gradient conjecture of R. Thom

Details Proof of the gradient conjecture of R. Thom Proof of the gradient conjecture of R. Thom

1999-06-30

arxiv.org/abs/math/9906212v2

Ann. of Math. (2) 152 (2000), no. 3, 763--792

Mathematics

Algebraic Geometry

30 pages, published version

Scientific paper

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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