Ilmari Kangasniemi

activity

20172026

most citedSharp cohomological bound for uniformly quasiregularly elliptic manifolds

9 citations · 35 across the 21 of their papers we have counts for

collaborators

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

math.DG2025

Quasiregular values and cohomology

Susanna Heikkilä, 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 $φ \in W_{loc}^{1, n} (Ω)$ , $Ω \subset R^{n}$ , that satisfy \[ \lvert\nabla φ(x)\rvert^n \le K(x)\bigl(\langle \nabla φ(x),…

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.MG2024

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 $μ$ with $μ (X) = \infty$ …

math.AP2024

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

Ilmari Kangasniemi

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

math.CV2024

Linear distortion and rescaling for quasiregular values

Ilmari Kangasniemi, Jani Onninen

Sobolev mappings exhibiting only pointwise quasiregularity-type bounds have arisen in various applications, leading to a recently developed theory of quasiregular values. In this a…

math.CV2023★ 2 cited

Corrigendum to "On the heterogeneous distortion inequality"

Ilmari Kangasniemi, Jani Onninen

We correct an error in [I. Kangasniemi, and J. Onninen, On the heterogeneous distortion inequality. Math. Ann. 384 (2022), no. 3-4, 1275-1308.]

math.CV2023

Quasiregular values and Rickman's Picard theorem

Ilmari Kangasniemi, Jani Onninen

We prove a far-reaching generalization of Rickman's Picard theorem for a surprisingly large class of mappings, based on the recently developed theory of quasiregular values. Our re…

math.AP2022★ 1 cited

Mappings of generalized finite distortion and continuity

Anna Doležalová, Ilmari Kangasniemi, Jani Onninen

We study continuity properties of Sobolev mappings $f \in W_{loc}^{1, n} (Ω, R^{n})$ , $n \geq 2$ , that satisfy the following generalized finite distortion inequality…

math.DG2022★ 2 cited

On the Moduli of Lipschitz Homology Classes

Ilmari Kangasniemi, Eden Prywes

We define a type of modulus $dMod_{p}$ for Lipschitz surfaces based on $L^{p}$ -integrable measurable differential forms, generalizing the vector modulus of Aikawa and Oh…

math.CV2022

A single-point Reshetnyak's theorem

Ilmari Kangasniemi, Jani Onninen

We prove a single-value version of Reshetnyak's theorem. Namely, if a non-constant map $f \in W_{loc}^{1, n} (Ω, R^{n})$ from a domain $Ω \subset R^{n}$ satisfies…

math.AP2022

Fibers of monotone maps of finite distortion

Ilmari Kangasniemi, Jani Onninen

We study topologically monotone surjective $W^{1, n}$ -maps of finite distortion $f : Ω \to Ω^{'}$ , where $Ω, Ω^{'}$ are domains in $R^{n}$ , $n \geq 2$ . If the outer distortion…

math.CV2021★ 1 cited

Notes on quasiregular maps between Riemannian manifolds

Ilmari Kangasniemi

These notes provide an exposition on obtaining the well-known standard results of quasiregular maps on Riemannian manifolds, given the corresponding theory in the Euclidean setting…

math.AP2021

Analytic characterization of monotone Hopf-harmonics

Ilmari Kangasniemi, Aleksis Koski, Jani Onninen

We study solutions of the inner-variational equation associated with the Dirichlet energy in the plane, given homeomorphic Sobolev boundary data. We prove that such a solution is m…

math.CV2021★ 6 cited

On the heterogeneous distortion inequality

Ilmari Kangasniemi, Jani Onninen

We study Sobolev mappings $f \in W_{loc}^{1, n} (R^{n}, R^{n})$ , $n \geq 2$ , that satisfy the heterogeneous distortion inequality \[\left|Df(x)\right|^n \leq K…

math.CV2020★ 2 cited

Conformally formal manifolds and the uniformly quasiregular non-ellipticity of $(S^{2} \times S^{2}) # (S^{2} \times S^{2})$

Ilmari Kangasniemi

We show that the manifold $(S^{2} \times S^{2}) # (S^{2} \times S^{2})$ does not admit a non-constant non-injective uniformly quasiregul…

math.MG2019★ 3 cited

Cheeger's differentiation theorem via the multilinear Kakeya inequality

David Bate, Ilmari Kangasniemi, Tuomas Orponen

Suppose that $(X, d, μ)$ is a metric measure space of finite Hausdorff dimension and that, for every Lipschitz $f : X \to R$ , $Lip (f, \cdot)$ is dominated…

math.DS2019★ 1 cited

Entropy in uniformly quasiregular dynamics

Ilmari Kangasniemi, Yûsuke Okuyama, Pekka Pankka +1

Let $M$ be a closed, oriented, and connected Riemannian $n$ -manifold, for $n \geq 2$ , which is not a rational homology sphere. We show that, for a non-constant and non-injective unif…

math.DG2019

Obstructions for automorphic quasiregular maps and Lattès-type uniformly quasiregular maps

Ilmari Kangasniemi

Suppose that $M$ is a closed, connected, and oriented Riemannian $n$ -manifold, $f : R^{n} \to M$ is a quasiregular map automorphic under a discrete group $Γ$ of Euclide…

math.PR2018

Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems

Diego Armentano, Jean-Marc Azaïs, Federico Dalmao +1

We obtain a Central Limit Theorem for the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size as the degree goes to infinity. A stud…

math.CV2017★ 9 cited

Sharp cohomological bound for uniformly quasiregularly elliptic manifolds

Ilmari Kangasniemi

We show that if a compact, connected, and oriented $n$ -manifold $M$ without boundary admits a non-constant non-injective uniformly quasiregular self-map, then the dimension of the…

math.CV2017★ 8 cited

Uniform cohomological expansion of uniformly quasiregular mappings

Ilmari Kangasniemi, Pekka Pankka

Let $f : M \to M$ be a uniformly quasiregular self-mapping of a compact, connected, and oriented Riemannian $n$ -manifold $M$ without boundary, $n \geq 2$ . We show that, for $k \i…

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

Quasiregular values and cohomology

Continuity for Sobolev mappings with null Lagrangian bounds

Warped products, solid hyperbolic fillings, and the identity D1,p=N1,p+R

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

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

Linear distortion and rescaling for quasiregular values

Corrigendum to "On the heterogeneous distortion inequality"

Quasiregular values and Rickman's Picard theorem

Mappings of generalized finite distortion and continuity

On the Moduli of Lipschitz Homology Classes

A single-point Reshetnyak's theorem

Fibers of monotone maps of finite distortion

Notes on quasiregular maps between Riemannian manifolds

Analytic characterization of monotone Hopf-harmonics

On the heterogeneous distortion inequality

Conformally formal manifolds and the uniformly quasiregular non-ellipticity of (S2×S2)#(S2×S2)

Cheeger's differentiation theorem via the multilinear Kakeya inequality

Entropy in uniformly quasiregular dynamics

Obstructions for automorphic quasiregular maps and Lattès-type uniformly quasiregular maps

Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems

Sharp cohomological bound for uniformly quasiregularly elliptic manifolds

Uniform cohomological expansion of uniformly quasiregular mappings

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

Conformally formal manifolds and the uniformly quasiregular non-ellipticity of $(S^{2} \times S^{2}) # (S^{2} \times S^{2})$