E. Le Donne

Non-smooth sub-Riemannian manifolds with non-integer dimension and a Poincar\'e inequality

For every integer $d\geq 3$ and real number $Q\in \left(d,\frac{d(d-1)+2}{2}\right]$, we construct a $Q$-Ahlfors regular metric measure manifold $(M,\mathbf{d},\mu)$ of topological dimension $d$ and analytic dimension $2$ that satisfies a Poincar\'e inequality. For every $Q>\frac{d(d-1)+2}{2}$, the construction yields...