Robert Young

activity

20052023

most citedFilling inequalities for nilpotent groups

21 citations · 98 across the 26 of their papers we have counts for

collaborators

33 papers

math.MG2023

The strong geometric lemma in the Heisenberg group

Vasileios Chousionis, Sean Li, Robert Young

We prove that in the first Heisenberg group, unlike Euclidean spaces and higher dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma for intrins…

math.MG2022

The Riesz tranform on intrinsic Lipschitz graphs in the Heisenberg group

Vasileios Chousionis, Sean Li, Robert Young

We prove that the Heisenberg Riesz transform is $L_{2}$ --unbounded on a family of intrinsic Lipschitz graphs in the first Heisenberg group $H$ . We construct this family by c…

math.MG2021

Undistorted fillings in subsets of metric spaces

Giuliano Basso, Stefan Wenger, Robert Young

We prove that if a quasiconvex subset $X$ of a metric space $Y$ has finite Nagata dimension and is Lipschitz $k$ -connected or admits Euclidean isoperimetric inequalities up to dime…

math.CA2021

Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group

Robert Young

In this paper, we give a necessary and sufficient condition for a graphical strip in the Heisenberg group $H$ to be area-minimizing in the slab ${- 1 < x < 1}$ . We show that…

math.CA2020

Harmonic intrinsic graphs in the Heisenberg group

Robert Young

Minimal surfaces in $R^{n}$ can be locally approximated by graphs of harmonic functions, i.e., functions that are critical points of the Dirichlet energy, but no analogous t…

math.MG2020

The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups

Vasileios Chousionis, Sean Li, Robert Young

We show that the $β$ --numbers of intrinsic Lipschitz graphs of Heisenberg groups $H_{n}$ are locally Carleson integrable when $n \geq 2$ . Our technique relies on a recent Do…