T. Rajala

activity

20242026

collaborators

5 papers

math.FA2026

Planar $W^{1, 1}$ -extension domains

Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang

We show that a bounded planar simply connected domain $I^c ◯$ is a $W^{1, 1}$ -extension domain if and only if for every pair $x, y$ of points in $I^c ◯^{c}$ there exists a curve $Î³\subset…

math.GN2025

Measure and dimension theory of permeable sets and its applications to fractals

Gunther Leobacher, Tapio Rajala, Alexander Steinicke +1

We study {\it permeable} sets. These are sets $Î\subset \mathbb{R}^d$ which have the property that each two points $x,y\in \mathbb{R}^d$ can be connected by a short path \(Î³\…

math.MG2025

Closed BV-extension and $W^{1, 1}$ -extension sets

Emanuele Caputo, Jesse Koivu, Danka LuÄiÄ +1

This paper studies the relations between extendability of different classes of Sobolev $W^{1, 1}$ and $B V$ functions from closed sets in general metric measure spaces. Under the ass…

math.MG2025

A note on Laplacian bounds, deformation properties and isoperimetric sets in metric measure spaces

Enrico Pasqualetto, Tapio Rajala

In the setting of length PI spaces satisfying a suitable deformation property, it is known that each isoperimetric set has an open representative. In this paper, we construct an ex…

math.CA2024

A geometric characterization of planar Sobolev extension domains