Ilmari Kangasniemi

activity

20242026

collaborators

7 papers

math.CV2026

Values of finite distortion: Reshetnyak's theorem, the Liouville theorem, and the Lusin (N) -property

Ilmari Kangasniemi, Jani Onninen, Yizhe Zhu

Let $I^c ◯ \subset R^{n}$ be a domain and $f \in W_{loc}^{1, n} (I^c ◯, R^{n})$ . We say that $f$ has a value of finite distortion at $y_{0} \in R^{n}$ if there exi…

math.DG2025

Quasiregular values and cohomology

Susanna HeikkilÃ¤, Ilmari Kangasniemi

We prove that the recently shown cohomological obstruction for quasiregular ellipticity has a generalization in the theory of quasiregular values. More specifically, if $M$ is a cl…

math.CV2025

Continuity for Sobolev mappings with null Lagrangian bounds

Ilmari Kangasniemi, Jani Onninen

We prove the continuity of Sobolev functions $I ¨ \in W_{loc}^{1, n} (I^c ◯)$ , $I^c ◯ \subset R^{n}$ , that satisfy \[ \lvert\nabla Ï(x)\rvert^n \le K(x)\bigl(\langle \nabla Ï…

math.MG2025

Warped products, solid hyperbolic fillings, and the identity $D^{1, p} = N^{1, p} + R$

Ilmari Kangasniemi, Josh Kline, Nageswari Shanmugalingam +1

We construct a large class of metric measure spaces $Z$ which satisfy the identity $D^{1, p} (Z) = N^{1, p} (Z) + R$ , i.e.\ any measurable function $u : Z \to R$ …

math.AP2025

A Bourgain-Brezis-Mironescu -type characterization for Sobolev differential forms

Ilmari Kangasniemi

Given a bounded domain $I^c ◯ \subset R^{n}$ , a result by Bourgain, Brezis, and Mironescu characterizes when a function $f \in L^{p} (I^c ◯)$ is in the Sobolev space $W^{1, p} (I^c ◯)$ bas…

math.MG2025

On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry

Ryan Gibara, Ilmari Kangasniemi, Nageswari Shanmugalingam

We study the large-scale behavior of Newton-Sobolev functions on complete, connected, proper, separable metric measure spaces equipped with a Borel measure $I^¼$ with $Î¼(X) = \inft…