The Analytic Minimal Rank Sard Conjecture

A Belotto da Silva; A Parusiński; L Rifford

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arXiv · 2208.01392

The Analytic Minimal Rank Sard Conjecture

A Belotto da Silva·A Parusiński·L Rifford

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Abstract

We obtain, under an additional assumption on the subanalytic abnormal distribution constructed in [4], a proof of the minimal rank Sard conjecture in the analytic category. It establishes that from a given point the set of points accessible through singular horizontal curves of minimal rank, which corresponds to the rank of the distribution, has Lebesgue measure zero. The minimal rank Sard Conjecture is equivalent to the Sard Conjecture for co-rank 1 distributions.

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A Belotto da Silva, A Parusiński, L Rifford. 2022-08-02. The Analytic Minimal Rank Sard Conjecture. https://arxiv.org/abs/2208.01392

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