P. Goldstein

activity

20112024

most citedCharacterizations of generalized John domains in

R^{n}

via metric duality

1 citations · 1 across the 10 of their papers we have counts for

collaborators

14 papers

math.GT2024

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…

math.CA2023

Constructing diffeomorphisms and homeomorphisms with prescribed derivative

Paweł Goldstein, Zofia Grochulska, Piotr Hajłasz

We prove that for any measurable mapping $T$ into the space of matrices with positive determinant, there is a diffeomorphism whose derivative equals $T$ outside a set of measure le…

math.MG2022

Smooth approximation of mappings with rank of the derivative at most $1$

Paweł Goldstein, Piotr Hajłasz

It was conjectured that if $f \in C^{1} (R^{n}, R^{n})$ satisfies $rank D f \leq m < n$ everywhere in $R^{n}$ , then $f$ can be uniformly approximated by…

math.CA2018

Jacobians of $W^{1, p}$ homeomorphisms, case $p = [n /2]$

Paweł Goldstein, Piotr Hajłasz

We investigate a known problem whether a Sobolev homeomorphism between domains in $R^{n}$ can change sign of the Jacobian. The only case that remains open is when $f\in W^{1…

math.CA2018

$C^{1}$ mappings in $R^{5}$ with derivative of rank at most $3$ cannot be uniformly approximated by $C^{2}$ mappings with derivative of rank at most 3

Paweł Goldstein, Piotr Hajłasz

We find a counterexample to a conjecture of Gałęski by constructing for some positive integers $m < n$ a mapping $f \in C^{1} (R^{n}, R^{n})$ satisfying $\mathrm{rank}\, Df\…

math.CA2018

Topologically nontrivial counterexamples to Sard's theorem

Paweł Goldstein, Piotr Hajłasz, Pekka Pankka

We prove the following dichotomy: if $n = 2, 3$ and $f \in C^{1} (S^{n + 1}, S^{n})$ is not homotopic to a constant map, then there is an open set $Ω \subset S^{n + 1}$ …

Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms

Constructing diffeomorphisms and homeomorphisms with prescribed derivative

Smooth approximation of mappings with rank of the derivative at most 1

Jacobians of W1,p homeomorphisms, case p=[n/2]

C1 mappings in R5 with derivative of rank at most 3 cannot be uniformly approximated by C2 mappings with derivative of rank at most 3

Topologically nontrivial counterexamples to Sard's theorem

Smooth approximation of mappings with rank of the derivative at most $1$

Jacobians of $W^{1, p}$ homeomorphisms, case $p = [n /2]$

$C^{1}$ mappings in $R^{5}$ with derivative of rank at most $3$ cannot be uniformly approximated by $C^{2}$ mappings with derivative of rank at most 3