About Me

This is the professional home page of Tony Liimatainen (mathematics). Here you can find information about my research and publications.

Research Interest

In my research I consider inverse problems and related problems in differential geometry. At the moment, I am focusing my research on inverse problems for nonlinear equations and geometric inverse problems.

Here are recent examples of my research:

The slides of the presentation are available here AIP Minimal surface slides

The slides of the presentation are available here IAS Minimal surface extended slides.

The slides of the presentation are available here Helsinki slides.

The slides of the presentations are available here Irvine 2024 slides and here Irvine 2021 slides. The recordings of the talks can be found from here Irvine 2024 presentation at YouTube and here Irvine 2021 presentation at YouTube.

Publications and preprints

All publications and preprints in inverse chronological order (recent updates on the publication status of [3], [4] and [8]):

  1. T. Liimatainen, M. Salo, Applications of the Stone-Weierstrass theorem in inverse problems, arXiv:2404.01152, (2024).

  2. C. I. Cârstea, T. Liimatainen, L. Tzou, The Calderón problem on Riemannian surfaces and of minimal surfaces, arXiv:2406.16944, (2024). Note: This replaces the earlier preprint “An inverse problem for general minimal surfaces”, by a much more general version and new results.

  3. Y. Kian, T. Liimatainen, Y-H. Lin, On determining and breaking the gauge class in inverse problems for reaction-diffusion equations, Forum of Mathematics, Sigma, (2024), https://doi.org/10.1017/fms.2024.18. Preprint arXiv:2303.16115

  4. T. Liimatainen, Y-H. Lin, Uniqueness results for inverse source problems of semilinear elliptic equations, Inverse Problems (2024), http://iopscience.iop.org/article/10.1088/1361-6420/ad3088. Preprint arXiv:2204.11774

  5. M. Lassas, T. Liimatainen, L. Potenciano-Machado, T. Tyni, An inverse problem for a semi-linear wave equation: a numerical study, Inverse Problems and Imaging, (2023), https://dx.doi.org/10.3934/ipi.2023022. Preprint: arXiv:2203.09427

  6. C. I. Cârstea, M. Lassas, T. Liimatainen, L. Oksanen, An inverse problem for the Riemannian minimal surface equation, Journal of Differential Equations, 379, 626-648, (2023), https://doi.org/10.1016/j.jde.2023.10.039. Preprint: arXiv:2203.09262

  7. A. Feizmohammadi, T. Liimatainen, Y-H. Lin, An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds, Annals of PDE, (2023), https://link.springer.com/article/10.1007/s40818-023-00153-w. Preprint: arXiv:2112.08305.

  8. M. Lassas, T. Liimatainen, L. Potenciano-Machado and T. Tyni, Stability estimates for inverse problems for semi-linear wave equations on Lorentzian manifolds, Accepted for publication in Analysis and PDE, arXiv:2106.12257, (2021).

  9. T. Liimatainen, L. Oksanen, Counterexamples to inverse problems for the wave equation, Inverse Problems and Imaging, (2021), https://dx.doi.org/10.3934/ipi.2021058. Preprint: arXiv:2101.10740

  10. T. Liimatainen, Y-H. Lin, M. Salo and T. Tyni, Partial data inverse problems for elliptic equations with fractional power type nonlinearities, Journal of Differential Equations, 306, 189-219, (2022), https://doi.org/10.1016/j.jde.2021.10.015. Preprint: arXiv:2012.04944

  11. T. Balehowsky, A. Kujanpää, M. Lassas and T. Liimatainen, An Inverse Problem for the Relativistic Boltzmann Equation, Communications in Mathematical Physics, (2022), https://doi.org/10.1007/s00220-022-04486-8. Preprint: arXiv:2011.09312

  12. K. Krupchyk, T. Liimatainen and M. Salo, Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds, Advances in Mathematics, 403, (2022), https://doi.org/10.1016/j.aim.2022.108362. Preprint: arXiv:2009.05699

  13. M. Lassas, T. Liimatainen, L. Potenciano-Machado and T. Tyni, Uniqueness and stability of an inverse problem for a semi-linear wave equation, 337, (2022), Journal of Differential Equations, https://doi.org/10.1016/j.jde.2022.08.010. Preprint: arXiv:2006.13193

  14. M. Lassas and T. Liimatainen, Conformal harmonic coordinates, arXiv:1912.08030, (2019), Accepted for publication in Communications in Analysis and Geometry.

  15. M. Lassas, T. Liimatainen, Y-H. Lin and M. Salo, Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations, (2020), Revista Matemática Iberoamericana, 37, no. 4, 1553-1580, https://doi.org/10.4171/RMI/1242. Preprint: arXiv:1905.02764

  16. M. Lassas, T. Liimatainen, Y-H. Lin and M. Salo, Inverse problems for elliptic equations with power type nonlinearities, journal de Mathématiques Pures et Appliquées, (2021), https://doi.org/10.1016/j.matpur.2020.11.006. Preprint: arXiv:1903.12562

  17. M. Lassas, T. Liimatainen and M. Salo, The Poisson embedding approach to the Calderón problem, Mathematische Annalen, (2019), https://doi.org/10.1007/s00208-019-01818-3. Preprint: arXiv:1806.04954

  18. D. Dos Santos Ferreira, Y. Kurylev, M. Lassas, T. Liimatainen and M. Salo, The linearized Calderón problem in transversally anisotropic geometries, International Mathematics Research Notices (IMRN), (2018). https://doi.org/10.1093/imrn/rny234. Preprint: arXiv:1712.04716

  19. V. Julin, T. Liimatainen and M. Salo, p-harmonic coordinates for Hölder metrics and applications, Communications in Analysis and Geometry, 25, No.2, (2017) 395–430, https://dx.doi.org/10.4310/CAG.2017.v25.n2.a5. Preprint: arXiv:1507.03874

  20. M. Lassas, T. Liimatainen and M. Salo, A Calderón type problem for the conformal Laplacian, Communications in Analysis and Geometry, 30, No. 5, (2022), 1121–1184, https://dx.doi.org/10.4310/CAG.2022.v30.n5.a6. Preprint arXiv:1612.07939

  21. C-Y. Guo and T. Liimatainen, Equivalence of quasiregular mappings on subRiemannian manifolds via the Popp extension, arXiv:1605.00916, (2016).

  22. T. Liimatainen and M. Salo, Local gauge conditions for ellipticity in conformal geometry, International Mathematics Research Notices (IMRN), 13, (2016), 4058-4077, https://doi.org/10.1093/imrn/rnv255. Preprint arXiv:1310.3666

  23. T. Liimatainen and M. Salo, n-harmonic coordinates and the regularity of conformal mappings, Mathematical Research Letters, 21, No.2, (2014), 341–361, https://dx.doi.org/10.4310/MRL.2014.v21.n2.a11. Preprint arXiv:1209.1285

  24. T. Liimatainen, On the Role of Riemannian Metrics in Conformal and Quasiconformal Geometry, Doctoral dissertation. Aalto University, ISBN 978-952-60-5033-1, (2013), http://urn.fi/URN:ISBN:978-952-60-5034-8. Preprint arXiv:1110.0639

  25. T. Liimatainen, Optimal Riemannian metric for a volumorphism and a mean ergodic theorem in complete global Alexandrov nonpositively curved spaces, AMS Contemporary Mathematics 584: Analysis, Geometry and Quantum Field Theory, (2012), 163–178, http://dx.doi.org/10.1090/conm/584. Preprint arXiv:1206.0368

  26. T. Liimatainen and M. Salo, Nowhere conformally homogeneous manifolds and limiting Carleman weights, Inverse Problems and Imaging 6, Issue 3, (2012), 523–530, https://dx.doi.org/10.3934/ipi.2012.6.523. Preprint arXiv:1011.2507

Alternatively, you can find my publications from:

Google Scholar link to my publications Tony Liimatainen at Google Scholar.

and

ArXiv link to my publications: Tony Liimatainen at arXiv.