4 papers
Quasiconformal uniformization and extension for planar trees
Fotis Ioannidis, Fotis Ioannidis Vyron Vellis, Vyron Vellis
A classical uniformization theorem of Ahlfors from 1963 asserts that every bounded turning planar arc is the image of the unit segment under a quasiconformal self-map of the plane.…
Sobolev spaces on snowtrees
Efstathios Konstantinos Chrontsios Garitsis, Vyron Vellis
We introduce a discrete-energy Sobolev space on Ahlfors regular snowtrees, a class of metric trees where every arc is a snowflake of the same ty…
Flatness, Menger curvature, and parametrization
Guy C. David, Vyron Vellis
We show that on linearly locally contractible (LLC) manifolds, the beta numbers (which describe unilateral flatness) are comparable to the theta numbers (which describe bilateral f…
Tangents to Lipschitz and Sobolev images
Matthew Badger, Jared Krandel, Vyron Vellis
We develop geometric versions of Rademacher and Calderon type differentiability theorems in two categories. A special case of our results is that for any Lipschitz or continuous $W…