Real Algebraic and Analytic Geometry

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175. Paweł Goldstein:
Gradient flow of a harmonic function in R3.


Submission: 2005, October 20.

In the paper I study the gradient field of a harmonic function $f$ in R3 in a neighbourhood of a critical point $0$. I show that the flow of $\nabla f$, as a mapping between level sets of $f$, is a stratified mapping -- that gives, in our case, an answer to the problem of stratifying the space of orbits of the field $\nabla f$ posed by R. Thom. I also show that the trajectories of $\nabla f$ having $0$ as a limit point satisfy the finiteness conjecture and have generalized \mbox{tangents at 0}.

Mathematics Subject Classification (2000): 37C10, 32B20, 37B35.

Keywords and Phrases: stratification, gradient, gradient conjecture, finiteness conjecture.

Full text, 36p.: ps.gz 318k, pdf 514k.

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