19 citations · 30 across the 10 of their papers we have counts for
15 papers
On CAT() surfaces
Saajid Chowdhury, Hechen Hu, Matthew Romney +1
We study the properties of surfaces: length metric spaces homeomorphic to a surface having curvature bounded above in the sense of satisfying the co…
Remarks on conformal modulus in metric spaces
Matthew Romney
We give an example of an Ahlfors -regular, linearly locally connected metric space homeomorphic to containing a nondegenerate continuum with zero capacity, in…
Polyhedral approximation and uniformization for non-length surfaces
Dimitrios Ntalampekos, Matthew Romney
We prove that any metric surface (that is, metric space homeomorphic to a 2-manifold with boundary) with locally finite Hausdorff 2-measure is the Gromov-Hausdorff limit of polyhed…
Polyhedral approximation of metric surfaces and applications to uniformization
Dimitrios Ntalampekos, Matthew Romney
We prove that any length metric space homeomorphic to a 2-manifold with boundary, also called a length surface, is the Gromov-Hausdorff limit of polyhedral surfaces with controlled…
Triangulating metric surfaces
Paul Creutz, Matthew Romney
We prove that any length metric space homeomorphic to a surface may be decomposed into non-overlapping convex triangles of arbitrarily small diameter. This generalizes a previous r…
The branch set of minimal disks in metric spaces
Paul Creutz, Matthew Romney
We study the structure of the branch set of solutions to Plateau's problem in metric spaces satisfying a quadratic isoperimetric inequality. In our first result, we give examples o…
Quasiconformal geometry and removable sets for conformal mappings
Toni Ikonen, Matthew Romney
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain that vanishes on a compact set $E \subs…
Uniformization with infinitesimally metric measures
Kai Rajala, Martti Rasimus, Matthew Romney
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces homeomorphic to . Given a measure on such a space,…
On the inverse absolute continuity of quasiconformal mappings on hypersurfaces
Dimitrios Ntalampekos, Matthew Romney
We construct quasiconformal mappings for which there is a Borel set of positive Lebesgue $…
Singular quasisymmetric mappings in dimensions two and greater
Matthew Romney
For all , we construct a metric space and a quasisymmetric mapping with the property that is not absolutely continuous wi…
Reciprocal lower bound on modulus of curve families in metric surfaces
Kai Rajala, Matthew Romney
We prove that any metric space homeomorphic to with locally finite Hausdorff 2-measure satisfies a reciprocal lower bound on modulus of curve families associated…
Quasiconformal parametrization of metric surfaces with small dilatation
Matthew Romney
We verify a conjecture of Rajala: if is a metric surface of locally finite Hausdorff 2-measure admitting some (geometrically) quasiconformal parametrization by a simply con…
Quasiconformal mappings on the Grushin plane
Chris Gartland, Derek Jung, Matthew Romney
We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it is metrically quasiconformal and if and only if it is geometrically quasiconformal. As t…
Conformal Grushin spaces
Matthew Romney
We introduce a class of metrics on generalizing the classical Grushin plane. These are length metrics defined by the line element for a…
Bi-Lipschitz embedding of the generalized Grushin plane in Euclidean spaces
Matthew Romney, Vyron Vellis
We show that, for all , the generalized Grushin plane is bi-Lipschitz homeomorphic to a -dimensional quasiplane in the Euclidean space $\mathbb{R}^{[α]+2…