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- W2957530950 abstract "<!-- *** Custom HTML *** --> We show that every subset of $mathbb{R}^n$ definable in an o-minimal structure can be decomposed into a finite number of definable sets that are quasi-convex i.e. have comparable, up to a constant, the intrinsic distance and the distance induced from the embedding. We apply this result to study the limits of secants of the trajectories of gradient vector field $nabla f$ of a $C^1$ definable function $f$ defined in an open subset of $mathbb{R}^n$. We show that if the o-minimal structure is polynomially bounded then the limit of such secants exists, that is an analog of the gradient conjecture of R. Thom holds. Moreover we prove that for $n = 2$ the result is true in any o-minimal structure." @default.
- W2957530950 created "2019-07-23" @default.
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- W2957530950 date "2019-03-06" @default.
- W2957530950 modified "2023-10-12" @default.
- W2957530950 title "Quasi-convex decomposition in o-minimal structures. Application to the gradient conjecture" @default.
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- W2957530950 doi "https://doi.org/10.2969/aspm/04310137" @default.
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