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A. Belotto da Silva - Singular foliations in sub-Riemannian geometry and the Strong Sard Conjecture

Given a totally nonholonomic distribution of rank two $\Delta$ on a three-dimensional manifold $M$, it is natural to investigate the size of the set of points $\mathcal{X}^x$ that can be reached by singular horizontal paths starting from a same point $x \in M$. In this setting, the Sard conjecture states that $\mathcal{X}^x$ should be a subset of the so-called Martinet surface of 2-dimensional Hausdorff measure zero. I will present a reformulation of the conjecture in terms of the behavior of a (real) singular ...
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