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math.CA2012
Gradient trajectories for plane singular metrics I: oscillating trajectories
Vincent Grandjean
We construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some…
math.CA2011★ 4 cited
On restricted Analytic Gradients on Analytic Isolated Surface Singularities
Vincent Grandjean, Fernando Sanz
Let (X,O) be a real analytic isolated surface singularity at the origin o of a real analytic manifold M equipped with a real analytic metric g. Given a real analytic function f:(M,…
math.CA2011
On Hessian limit directions along non-oscillating gradient trajectories
Vincent Grandjean
Given a non-oscillating gradient trajectory G of a real analytic function f, we show that the limit v of the secants at the limit point O of G along the trajectory G is an eigen-ve…