Research
My research interests lie at the interface of geometry and analysis, including classical complex analysis, the geometry of negatively curved spaces, geometric group theory, dynamics of rational maps, and analysis on metric spaces. My current work often relies on an extension of classical results in geometry and analysis to a non-smooth or fractal setting.
Research Seminars
Sylvester Eriksson-Bique, Misha Hlushchanka, Annina Iseli, and I are running an international Zoom research seminar "Quasiworld". The topics include quasiconformal geometry, complex dynamics, and analysis on metric spaces. For more
information see:
Quasiworld.
I also organize a similar Zoom seminar ``Pacific Quasiworld" (adapted to time zones in Asia) together with Yunping Jiang, Zhiqiang Li, and Mitsu Shishikura.
See: Pacific Quasiworld.
Research Monograph
- M. Bonk and D. Meyer, Expanding Thurston maps, Mathematical Surveys and Monographs, Vol. 225, Amer. Math. Soc., Providence, RI, 2017, 478 pp. Available here: Expanding Thurston Maps
Research papers after 2010
- M. Bonk, D. Meyer, and
M. Hlushchanka, Quasi-visual approximations, Preprint, January 2026,
(arXiv link).
- M. Bonk, Conformal maps and critical points of Eisenstein series, Preprint, June 2025,
(arXiv link).
- M. Bonk, M. Hlushchanka, and R. Lodge, Thurston's pullback map, invariant covers, and the global dynamics on curves, Preprint, November 2024, to appear in: Proc. Amer. Math. Soc. (arXiv link).
- M. Bonk, J. Junnila, S. Rohde, and Y. Wang, Piecewise geodesic Jordan curves II: Loewner energy, projective structures, and accessory parameters, Preprint, October 2024, to appear in: Invent. Math. (arXiv link).
- M. Bonk, L. Capogna, and X. Zhou, Green functions in metric measure spaces, Preprint, November 2022, (arXiv link).
- M. Bonk, The quasi-periods of the Weierstrass zeta-function, Enseign. Math. 71 (2025), 335--364. Corrected version: (arXiv link).
- M. Bonk, M. Hlushchanka, and A. Iseli, Eliminating Thurston obstructions and controlling dynamics on curves, Ergod. Th. & Dynam. Sys. 44 (2024), 2454--2532, (arXiv link).
- M. Bonk and D. Meyer, Uniformly branching trees, Trans. Amer. Math. Soc. 375 (2022), 3841-3897, (arXiv link).
- M. Bonk and A. Eremenko, Canonical embeddings of pairs of arcs, Comput. Methods Funct. Theory 21 (2021), 825-830, (arXiv link).
- M. Bonk and H. Tran, The continuum self-similar tree, in: Fractal Geometry and Stochastics VI (Eds. U. Freiberg et al.), Birkhäuser, Cham, 2021, pp. 143--189, (arXiv link).
- M. Bonk and D. Meyer, Quotients of torus endomorphisms and Lattès-type maps, Arnold Math. J. 6 (2020), 495-521, (arXiv link).
- M. Bonk and S. Merenkov, Square Sierpinski carpets and Lattès maps, Math. Z. 296 (2020), 695-718, (arXiv link).
- M. Bonk and D. Meyer, Quasiconformal and geodesic trees, Fundamenta Math. 250 (2020), 253-299, (arXiv link).
- M. Bonk, L. Capogna, P. Hajlasz, N. Shanmugalingam, and J. Tyson, Analysis on metric spaces, Notices Amer. Math. Soc. 67 (2020), 253-256, (arXiv link).
- M. Bonk and P. Poggi-Corradini, The Rickman-Picard Theorem, Annales Acad. Sci. Fennicae 44 (2019), 615-633, (arXiv link).
- M. Bonk, E. Saksman, and T. Soto, Triebel-Lizorkin spaces on metric spaces via hyperbolic fillings, Indiana Univ. Math. J. 67 (2018), 1625-1663, (arXiv link).
- M. Bonk and E. Saksman, Sobolev spaces and hyperbolic fillings, J. Reine Angew. Math. 737 (2018), 161-187, (arXiv link).
- M. Bonk, Uniformization by square domains, J. Analysis 24 (2016), 103-110, (arXiv link).
- M. Bonk, M. Lyubich, and S. Merenkov, Quasisymmetries of Sierpinski carpet Julia sets, Adv. Math. 301 (2016), 383-422, (arXiv link).
- M. Bonk and S. Merenkov, Quasisymmetric rigidity of square Sierpinski carpets, Ann. of Math. 177 (2013), 591-643, (arXiv link).
- M. Bonk, Uniformization of Sierpinski carpets in the plane, Invent. Math. 186 (2011), 559-665, (arXiv link).