18 citations · 62 across the 31 of their papers we have counts for
8 papers · 1 filter
Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms
Paweł Goldstein, Zofia Grochulska, Piotr Hajłasz
Cerf and Palais independently proved a remarkable result about extending diffeomorphisms defined on smooth balls in a manifold to global diffeomorphisms of the manifold onto itself…
On the Gromov non-embedding theorem
Piotr Hajłasz, Armin Schikorra
We develop a new method leading to an elementary proof of a generalization of Gromov's theorem about non existence of Hölder embeddings into the Heisenberg group.
Linking topological spheres
Piotr Hajłasz
There is a topological embedding such that . Therefore, no -sphere can be linked with $ι(\mathbb{S}^…
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…
Sobolev Embedding of a Sphere Containing An Arbitrary Cantor Set in the image
Piotr Hajłasz, Xiaodan Zhou
We construct a large class of pathological -dimensional topological spheres in by showing that for any Cantor set there is a top…
On conditions for unrectifiability of a metric space
Piotr Hajłasz, Soheil Malekzadeh
We find necessary and sufficient conditions for a Lipschitz map , into a metric space to have the image with the -dimensional Hausdorff measure equal zero, $…
Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces
Piotr Hajlasz, Armin Schikorra
We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not…
Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups
Piotr Hajlasz, Armin Schikorra, Jeremy T. Tyson
We provide a sufficient condition for the nontriviality of the Lipschitz homotopy group of the Heisenberg group, , in terms of properties of the classical homotopy…