2 citations · 3 across the 3 of their papers we have counts for
14 papers
Lusin-type properties of convex functions and convex bodies
Daniel Azagra, Piotr Hajłasz
We prove that if is convex and has finite measure, then for any there is a convex function $g:\mathbb{R}^n\to\m…
On an old theorem of Erdös about ambiguous locus
Piotr Hajłasz
Erdös proved in 1946 that if a set is closed and non-empty, then the set, called ambiguous locus or medial axis, of points in with the propert…
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…
Linking topological spheres
Piotr Hajłasz
There is a topological embedding such that . Therefore, no -sphere can be linked with $ι(\mathbb{S}^…
Sobolev embedding for spaces is equivalent to a lower bound of the measure
Ryan Alvarado, Przemysław Górka, Piotr Hajłasz
It has been known since 1996 that a lower bound for the measure, , implies Sobolev embedding theorems for Sobolev spaces defined on metric-measure spa…
A note on metric-measure spaces supporting Poincaré inequalities
Ryan Alvarado, Piotr Hajłasz
Using a method of Korobenko, Maldonado and Rios we show a new characterization of doubling metric-measure spaces supporting Poincaré inequalities without assuming a priori that the…