4 problems

Dimension-free cut-locus structure conjecture. The cut locus has the form

A Carnot group is a graded nilpotent Lie group, and its subRiemannian geodesic flow is the geodesic flow associated with its subRiemannian structure. Complete integrability conject…

Microregular germs conjecture. The following hold:

Let $\mathfrak L$ be a stratified Lie group equipped with its canonical Carnot–Carathéodory distance function, and let $\Upomega$ be a domain. Assume that $\mathfrak L$ is neither…