Author

S. Eriksson-Bique

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Preprint Oct 2026

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...

S. Eriksson-Bique, E. Le Donne · 0 citations

Preprint Sep 2026

On universal elements for doubling geodesic trees

For $n\ge 3$ and $c\in(0,1)$, let $\mathcal{GT}(n,c)$ denote the class of geodesic metric trees of valence at most $n$ whose branch points are uniformly relatively separated with constant $c$. We prove that $\mathcal{GT}(n,c)$ has no bi-Lipschitz universal element. More precisely, we construct a family $(T_a)_{a\in[1/4...

S. Eriksson-Bique, Manisha Garg · 0 citations