Subdifferentials and Minimizing Sard Conjecture in Sub-Riemannian Geometry

TL;DR

This paper uses advanced mathematical techniques to identify new classes of sub-Riemannian structures that satisfy the Minimizing Sard conjecture, expanding understanding in geometric measure theory.

Contribution

It demonstrates that complete sub-Riemannian structures with certain distribution ranks satisfy the Minimizing Sard conjecture, providing new examples and insights.

Findings

Structures with co-rank 2 satisfy the conjecture

Generic distributions of rank ≥ 2 satisfy the conjecture

New examples of structures fulfilling the conjecture

Abstract

We use techniques from nonsmooth analysis and geometric measure theory to provide new examples of complete sub-Riemannian structures satisfying the Minimizing Sard conjecture. In particular, we show that complete sub-Riemannian structures associated with distributions of co-rank 2 or generic distributions of rank $\ge$ 2 satisfy the Minimizing Sard conjecture.