Matthew Romney

collaborators

2 papers

math.MG2024

Graphs that are not minimal for conformal dimension

Matthew Romney

We construct functions $f : [0, 1] \to [0, 1]$ whose graph as a subset of $R^{2}$ has Hausdorff dimension greater than any given value $α \in (1, 2)$ but conformal dimensio…

math.MG2022

Remarks on conformal modulus in metric spaces

Matthew Romney

We give an example of an Ahlfors $3$ -regular, linearly locally connected metric space homeomorphic to $R^{3}$ containing a nondegenerate continuum $E$ with zero capacity, in…