206 citations · 394 across the 45 of their papers we have counts for
18 papers · 1 filter
Extension properties of planar subsets supporting a weak -Poincaré inequality
Miguel García-Bravo, Tapio Rajala
We study Sobolev and -extension properties of planar subsets. In particular, we prove that fat Sierpiński carpets that support a weak -Poincaré inequality are -…
Closed BV-extension and -extension sets
Emanuele Caputo, Jesse Koivu, Danka Lučić +1
This paper studies the relations between extendability of different classes of Sobolev and functions from closed sets in general metric measure spaces. Under the ass…
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…
Approximation by BV-extension sets via perimeter minimization in metric spaces
Jesse Koivu, Danka Lučić, Tapio Rajala
We show that every bounded domain in a metric measure space can be approximated in measure from inside by closed -extension sets. The extension sets are obtained by minimizing…
Non-Hilbertian tangents to Hilbertian spaces
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.
Strong -extension and -extension domains
Miguel García-Bravo, Tapio Rajala
We show that a bounded domain in a Euclidean space is a -extension domain if and only if it is a strong -extension domain. In the planar case, bounded and strong -…
Approximation by uniform domains in doubling quasiconvex metric spaces
Tapio Rajala
We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.
Indecomposable sets of finite perimeter in doubling metric measure spaces
Paolo Bonicatto, Enrico Pasqualetto, Tapio Rajala
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak -Poincaré inequality. Th…
Sharp estimate on the inner distance in planar domains
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
We show that the inner distance inside a bounded planar domain is at most the one-dimensional Hausdorff measure of the boundary of the domain. We prove this sharp result by establi…
Optimal transport maps on Alexandrov spaces revisited
Tapio Rajala, Timo Schultz
We give an alternative proof for the fact that in -dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely $(n-1)…
Products of snowflaked euclidean lines are not minimal for looking down
Matthieu Joseph, Tapio Rajala
We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and…
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
Enrico Le Donne, Tapio Rajala, Erik Walsberg
We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space isometricall…
Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces
Enrico Le Donne, Sean Li, Tapio Rajala
We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Questio…
Tangent lines and Lipschitz differentiability spaces
Fabio Cavalletti, Tapio Rajala
We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces. We first revisit the almost everywhere me…
Failure of topological rigidity results for the measure contraction property
Christian Ketterer, Tapio Rajala
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. Th…
Assouad dimension, Nagata dimension, and uniformly close metric tangents
Enrico Le Donne, Tapio Rajala
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by…
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below
Nicola Gigli, Andrea Mondino, Tapio Rajala
We show that in any infinitesimally Hilbertian -space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space…
Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces
Luigi Ambrosio, Tapio Rajala
We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slop…