Authors
Citation
K. Kurdyka et al., Proof of the gradient conjecture of R. Thom, ANN MATH, 152(3), 2000, pp. 763-792
Citations number
24
Categorie Soggetti
Mathematics
Journal title
ANNALS OF MATHEMATICS
ISSN journal
0003486X
→ ACNP
Volume
152
Issue
3
Year of publication
2000
Pages
763 - 792
Database
ISI
SICI code
0003-486X(200011)152:3<763:POTGCO>2.0.ZU;2-L
Abstract
Let x(t) be a trajectory of the gradient of a real analytic function and su
ppose that to is a limit point of x(t). We prove the gradient conjecture of
R. Them which states that the secants of x(t) at to have a limit. Actually
we show a stronger statement: the radial projection of x(t) from to onto t
he unit sphere has finite length.