Abnormal singular foliations and the Sard conjecture for generic co-rank one distributions
Given a smooth totally nonholonomic distribution on a smooth manifold, we construct a singular distribution capturing essential abnormal lifts which is locally generated by vector fields with controlled divergence. Then, as an application, we prove the Sard conjecture for rank 3 distribution in dimension 4 and generic distributions of corank 1 .
Authors
- Ludovic Rifford (ORCID: https://orcid.org/0000-0003-2084-7471)
- Adam Parusiński (ORCID: https://orcid.org/0000-0002-8203-2561)
- André Belotto da Silva (ORCID: https://orcid.org/0000-0002-4203-6154)
Institutions
- Institut Universitaire de France (FR)
- Université Côte d'Azur (FR)
- Institut de Mathématiques de Jussieu-Paris Rive Gauche (FR)
- Observatoire de la Côte d’Azur (FR)
Publication Details
- Journal
- Revista Matemática Iberoamericana
- Published
- 2025-07-01
- DOI
- https://doi.org/10.4171/rmi/1567
- Primary Topic
- Advanced Differential Equations and Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00