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On restricted Analytic Gradients on Analytic Isolated Surface Singularities | | Vincent Grandjean
; Fernando Sanz
; | | Date: |
19 May 2011 | | Abstract: | 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,O) --> (R,0) singular at O, we prove that the gradient
trajectories for the metric g|(X,O) of the restriction f|X escaping from or
ending up at the origin O do not oscillate. Such a trajectory is thus a
sub-pfaffian set. Moreover, in each connected component of XO where the
restricted gradient does not vanish, there is always a trajectory accumulating
at O and admitting a formal asymptotic expansion at O | | Source: | arXiv, 1105.3888 | | Services: | Forum | Review | PDF | Favorites | |
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