1 citations · 1 across the 4 of their papers we have counts for
9 papers
A Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group
Gareth Speight, Scott Zimmerman
We characterize which mappings from a compact subset of into the Heisenberg group can be extended to a horizontal curve for a given modulus of continuity …
Singular integrals on regular curves in Banach duals
Scott Zimmerman
The modern study of singular integral operators on curves in the plane began in the 1970's. Since then, there has been a vast array of work done on the boundedness of singular inte…
Singular integrals on regular curves in Carnot groups
Vasileios Chousionis, Sean Li, Scott Zimmerman
Let be any Carnot group. We prove that if a convolution type singular integral associated with a -dimensional Calderón-Zygmund kernel is -bounded on horizontal…
Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces
Vasileios Chousionis, Sean Li, Vyron Vellis +1
The Heisenberg group equipped with a sub-Riemannian metric is one of the most well known examples of a doubling metric space which does not admit a bi-Lipschitz embedd…
An implicit function theorem for Lipschitz mappings into metric spaces
Piotr Hajłasz, Scott Zimmerman
We prove a version of the implicit function theorem for Lipschitz mappings into arbitrary metric spaces. As long as the pull-back of the Hausdor…
A Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group
Andrea Pinamonti, Gareth Speight, Scott Zimmerman
We characterize those mappings from a compact subset of into the Heisenberg group which can be extended to a horizontal curve in $\mathbb{H}^{…