Postdoctoral Researcher in Mathematics | University of Fribourg
I am currently a postdoctoral researcher at the University of Fribourg.
My research interests lie at the interaction of analysis and geometry, with an emphasis on potential analysis and quasiconformal geometry.
I completed my PhD in 2022 at the University of Jyväskylä under the supervision of Professor Kai Rajala.
first order Sobolev spaces in metric measure spaces with applications to potential analysis
quasiconformal geometry: uniformization problems for two-dimensional metric surfaces
interactions of geometric mapping theory and isoperimetric inequalities, especially in the context of quasiregular curves
My publication lists are available on my ORCID page and on my MathSciNet and Google Scholar profiles. I am also on Researchgate.
Preprints (submitted):
(2025) Toni Ikonen. Entire conformal curves are affine or have super-Euclidean energy growth. arXiv preprint
(2025) Miguel García-Bravo, Toni Ikonen, Zheng Zhu. Infinity thick quasiconvexity and applications. arXiv preprint
(2025) Eero Hakavuori, Susanna Heikkilä, Toni Ikonen. Smooth contact lifts and central extensions of Carnot groups. arXiv preprint
(2024) Toni Ikonen. Pushforward of currents under Sobolev maps. arXiv preprint
To appear:
Toni Ikonen, Pekka Pankka. Liouville's theorem in calibrated geometries. Journal d'Analyse Mathématique. arXiv preprint
Publications:
(2025) Ikonen, T. Quasiregular Curves: Removability of Singularities. J Geom Anal 35, 315. https://doi.org/10.1007/s12220-025-02146-6
(2025) Ambrosio, L., Ikonen, T., Lučić, D., Pasqualetto, E. Correction to: Metric Sobolev Spaces I: Equivalence of Definitions, Milan J. Math. https://doi.org/10.1007/s00032-025-00422-2
(2024) Ambrosio, L., Ikonen, T., Lučić, D., Pasqualetto, E. Metric Sobolev Spaces I: Equivalence of Definitions, Milan J. Math. (2024). https://doi.org/10.1007/s00032-024-00407-7
(2023) Esmayli, B. and Ikonen, T. and Rajala, K. Coarea inequality for monotone functions on metric surfaces. Trans. Amer. Math. Soc. 376, 7377--7406. https://doi.org/10.1090/tran/8998
(2022) Ikonen, T., Romney, M. Quasiconformal geometry and removable sets for conformal mappings (2022). JAMA 148, 119–185. https://doi.org/10.1007/s11854-022-0224-5
(2022) Ikonen, T., Two-dimensional metric spheres from gluing hemispheres. J. London Math. Soc., 106: 3069-3102. https://doi.org/10.1112/jlms.12656
(2022) Ikonen, T., Uniformization of metric surfaces using isothermal coordinates. Annales Fennici Mathematici, 47(1), 155-180. https://doi.org/10.54330/afm.112781
(2022) Ikonen, T., Pasqualetto, E., & Soultanis, E. Abstract and concrete tangent modules on Lipschitz differentiability spaces. Proceedings of the American Mathematical Society, 150, 327-343. https://doi.org/10.1090/proc/15656
(2021) Ikonen, T. Quasiconformal Jordan Domains. Analysis and Geometry in Metric Spaces, 9(1), 167-185. https://doi.org/10.1515/agms-2020-0127
(08/2024) Metric Geometry and Geometry Measure Theory, Fribourg, Switzerland
(07/2024) Geometry and Analysis on Metric Surfaces, IMPAN, Poland
(06/2024) Geometric Measure Theory and Applications 2024, Cortona, Italy
(05/2024) AGENTForum 2024, University of Jyväskylä, Finland
(01/2024) Finnish Mathematical Days, 2024, Aalto University, Finland
(04/2023) Fribourg MAPS, University of Fribourg, Switzerland
(11/2022) Quasiworld seminar, UCLA (online)
(08/2022) 28th Nordic Congress of Mathematicians, Aalto University, Finland
(10/2021) AGENT Forum 2021, Aalto University, Finland
Linear algebra and matrix calculus III, University of Helsinki (2024)
Linear algebra and matrix calculus III, University of Helsinki (2023)
Complex calculus, University of Jyväskylä (2022)
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