Analysis Seminar
Speaker: Vincent Grandjean (Fields Institute)
"Gradient trajectories on isolated surface singularities do not oscillate at their limit point"
Time: 15:30
Room: MC 107
Consider Rn equipped with a real analytic Riemannian metric g. Let f:Rn→R be a real analytic function singular at O the origin. We would like to understand the dynamics of ∇f in a neighbourhood of the critical point O, where ∇f stands for the gradient vector field of the function f associated with the metric g. We are particularly interested in the oscillating/non-oscillating behaviour in a neighbourhood of O of any gradient trajectory accumulating on O.
We prove that if a trajectory lies in a real analytic surface with an isolated singularity at O, then it cannot oscillate at O.
In the first talk, I will recall elementary and well known facts and ideas about the gradient problem. In the second one, I will sketch the proof of our theorem.
This is joint work with Fernando Sanz (Valladolid).