P. Hajłasz

activity

20062026

most citedSobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target

18 citations · 62 across the 31 of their papers we have counts for

collaborators

Showing math.CAShow all

12 papers · 1 filter

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.CA2020

Lusin-type properties of convex functions and convex bodies

Daniel Azagra, Piotr Hajłasz

We prove that if $f : R^{n} \to R$ is convex and $A \subset R^{n}$ has finite measure, then for any $ε > 0$ there is a convex function $g:\mathbb{R}^n\to\m…

math.CA2020

On an old theorem of Erdös about ambiguous locus

Piotr Hajłasz

Erdös proved in 1946 that if a set $E \subset R^{n}$ is closed and non-empty, then the set, called ambiguous locus or medial axis, of points in $R^{n}$ with the propert…

math.CA2020

The Coarea Inequality

Behnam Esmayli, Piotr Hajłasz

The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not a…

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 $Ω \subset S^{n + 1}$ …

math.CA2018

Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion

Paweł Goldstein, Piotr Hajłasz

In the paper we investigate continuity of Orlicz-Sobolev mappings $W^{1, P} (M, N)$ of finite distortion between smooth Riemannian $n$ -manifolds, $n \geq 2$ , under the assumption that…

math.CA2017

Finite distortion Sobolev mappings between manifolds are continuous

Paweł Goldstein, Piotr Hajłasz, Mohammad Reza Pakzad

We prove that if $M$ and $N$ are Riemannian, oriented $n$ -dimensional manifolds without boundary and additionally $N$ is compact, then Sobolev mappings $W^{1, n} (M, N)$ of finite dis…

math.CA2017

Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian

Paweł Goldstein, Piotr Hajłasz

We construct an a.e. approximately differentiable homeomorphism of a unit $n$ -dimensional cube onto itself which is orientation preserving, has the Lusin property (N) and has the J…

math.CA2015

A measure and orientation preserving homeomorphism with approximate Jacobian equal $- 1$ almost everywhere

Paweł Goldstein, Piotr Hajłasz

We construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit $n$ -dimensional cube onto itself, whose Jacobian is equal…

math.CA2015★ 1 cited

The Dubovitski\uı-Sard Theorem in Sobolev Spaces

Piotr Hajłasz, Scott Zimmerman

The Sard theorem from 1942 requires that a mapping $f : R^{n} \to R^{m}$ is of class $C^{k}$ , $k > max (n - m, 0)$ . In 1957 Duvovitski\uı generalized Sard's theorem to the…

Constructing diffeomorphisms and homeomorphisms with prescribed derivative

Lusin-type properties of convex functions and convex bodies

On an old theorem of Erdös about ambiguous locus

The Coarea Inequality

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

Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion

Finite distortion Sobolev mappings between manifolds are continuous

Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian

A measure and orientation preserving homeomorphism with approximate Jacobian equal −1 almost everywhere

The Dubovitski\uı-Sard Theorem in Sobolev Spaces

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

A measure and orientation preserving homeomorphism with approximate Jacobian equal $- 1$ almost everywhere