The Analytic Minimal Rank Sard Conjecture
Differential Geometry
2025-01-14 v2 Optimization and Control
Symplectic Geometry
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.
Cite
@article{arxiv.2208.01392,
title = {The Analytic Minimal Rank Sard Conjecture},
author = {A Belotto da Silva and A Parusiński and L Rifford},
journal= {arXiv preprint arXiv:2208.01392},
year = {2025}
}
Comments
Important: The previous paper had two sets of distinct results. We have divided the paper in two, and this version contains the second set of results. The first part will appear in a new hal submission hal-04881557. The title has changed