5 problems

In the Martinet case, the cut-locus is the set of endpoints where minimizing geodesics cease to be minimizing; in the generic case, the northern hemisphere and the end-point of the…

Let $\mathbb F_4$ be the free step-2 rank-four Carnot group, and let $\mathcal H$ be the union of all strict Carnot subgroups. Equivalently, … Let…

Let $\pi:\mathbb{S}^{2n+1}\to\mathbb{CP}^n$ be the quotient map, let … and set $\tilde{X}(d)=\pi^{-1}(X(d))$. Here $\mathbb{Z}_d^{\star(n+1)}$ denotes the $(n+1)$-fold topological…

Let $P(\beta)$ be the period function in $G_\alpha$, with $\beta$ the parameter used to specify the initial tangent vector. The period-function conjecture. … and … The source estab…

Let $\mathbb{G}_k$ be the free step-two Carnot group of rank $k$, identified with $\mathbb{R}^k\oplus\wedge^2\mathbb{R}^k$, and let $\mathrm{Cut}_0(\mathbb{G}_k)$ denote its cut lo…