## Pekka PankkaProfessor ## Contact information
Room: D325 ## TeachingSpring 2023: De Rham theoryFall 2022 (Period II) Lineaarialgebra ja matrisiilaskenta I Fall 2022 (Period I): Raja-arvot Fall 2021 (Period II): Lineaarialgebra ja matriisilaskenta I [Lecture notes for Lineaarialgebra ja metriisilaskenta I-III] Fall 2021 (Period I): Raja-arvot Spring 2021 (Period IV): Lineaarialgebra ja matriisilaskenta III Spring 2021 (Period III): Lineaarialgebra ja matriisilaskenta II Fall 2020 (Period II): Lineaarialgebra ja matriisilaskenta I Spring 2020 (Period IV): Lineaarialgebra ja matriisilaskenta III Spring 2020 (Period III): Integraalilaskenta Spring 2019: Topologia Ia & Ib Spring 2018: Topologia Ia & Ib Fall 2016: Topologia Ia and Topologia Ib Fall 2015 (Jyväskylä): Degree theory and Branched covers [Lecture notes from 2017] Fall 2014 (Jyväskylä): Perusryhmä ja peiteavaruus Fall 2013 (Jyväskylä): Introduction to de Rham cohomology ## Preprints- De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean (with Susanna Heikkilä) [arXiv:2302.11440]
- Deep Invertible Approximation of Topologically Rich Maps between Manifolds
(with Michael Puthwala, Matti Lassas,
Ivan Dokmanic,
and Maarten de Hoop) [arXiv:2210.00577]
- Quasiregular Curves of Small Distortion in Product Manifolds
(with Susanna Heikkilä and Eden Prywes ) [arXiv:2106.11871]
- Transformation Optics for the Modelling of Waves in a Universe with Nontrivial Topology (with Tracey Balehowsky, Matti Lassas, and Ville Sirviö) [arXiv:2011.09547]
- Ahlfors reflection theorem for p-morphisms (with Pekka Koskela and Yi Zhang).
- Vertical quasi-isometries and branched quasisymmetries (with Jeff Lindquist).
- Deformation and quasiregular extension of cubical Alexander maps (with Jang-Mei Wu).
- Harmonic extensions of quasiregular maps (with Juan Souto).
## Publications- Bubbling of quasiregular maps (with Juan Souto).
*Math. Ann. (to appear)*[arXiv:1904.00885] - Quasiregular curves: Hölder continuity and higher integrability (with Jani Onninen).
*Complex Anal. Synerg. 7(3), 2021*[arXiv:2006.09340]
- A Neohookean model of plates (with Tadeusz Iwaniec, Jani Onninen, and Teresa Radice).
*SIAM J. Math. Anal. 53(1), 2021*[arXiv:2004.03381]
- Bing meets Sobolev (with Jani Onninen).
*Rev. Mat. Iberoameracana 37(5), 2021*[arXiv:1908.09193] - Entropy in uniformly quasiregular dynamics (with Ilmari Kangasniemi, Yûsuke Okuyama, and Tuomas Sahlsten). Ergodic Theory Dynam. Systems 41(8), 2021 [arXiv:1903.10183]
- Metric currents and polylipschitz forms (with Elefterios Soultanis). Calc. Var. Partial Differential Equations (to appear) [arXiv:1902.06106]
- Quasiregular curves.
*Ann. Acad. Sci. Fenn. (to appear)*[arXiv:1909.08221] [slides]
- Pull-back of metric currents and homological boundedness of BLD-elliptic spaces (with Elefterios Soultanis).
*Anal. Geom. Metr. Spaces 7(1)*[arXiv:1809.03009] - Stoilow's theorem revisited (with Rami Luisto).
*Expos. Math.*(to appear) [arXiv:1701.05726]
- Uniform cohomological expansion of uniformly quasiregular mappings (with Ilmari Kangasniemi).
*Proc. London Math. Soc. 118(3), 2019.*[arXiv:1708.01451]
- Free vs. Locally Free Kleinian Groups (with Juan Souto).
*J. Reine Angew. Math. 746, 2019.*[arXiv:1506.00156]
- Topologically nontrivial counterexamples to Sard's theorem (with Paweł Goldstein and Piotr Hajłasz ).
*IMRN, rny179, 2018.*[arXiv:1804.07658]
- Local monodromy of branched covers and dimension of the branch set (with Martina Aaltonen).
*Ann. Acad. Sci. Fenn. 42, 2017.*[arXiv:1509.06617]
- Quasiconformal non-parametrizability of almost smooth spheres (with Vyron Vellis).
*Selecta Math. 23(2), 2017.*[arXiv:1505.05293]
- Rigidity of extremal quasiregularly elliptic manifolds (with Rami Luisto).
*Groups Geom. Dyn. 10(2)*, 2016. [arXiv:1307.7940]
- Sharpness of Rickman's Picard theorem in all dimensions (with David Drasin).
*Acta Math. 214(2)*, 2015. [arXiv:1304.6998] [slides]
- Rescaling principle for isolated essential singularities of quasiregular mappings (with Yûsuke Okuyama).
*Proc. Amer. Math. Soc. 143, 2015.*[arXiv:1211.2977]
- Quasiregular ellipticity of open and generalized manifolds (with Kai Rajala and Jang-Mei Wu).
*Comput. Methods Funct. Theory 14, 2-3 (Gehring Memorial Volume)*, 2014. [arXiv:1310.8595]
- Geometry and quasisymmetric parametrization of Semmes spaces (with Jang-Mei Wu).
*Rev. Mat. Iberoameracana 30(3), 2014.*[arXiv:1111.2197]
- Equilibrium measures for uniformly quasiregular dynamics (with Yûsuke Okuyama).
*J. London Math. Soc. 89(2), 2014.*[arXiv:1204.6503]
- Distributional limits of Riemannian manifolds and graphs with sublinear genus growth (with Hossein Namazi and Juan Souto).
*Geom. Funct. Anal. 24(1), 2014.*[arXiv:1208.2130]
- Closed BLD-elliptic manifolds have virtually Abelian fundamental groups (with Enrico Le Donne).
*New York J. Math. 20*, 2014. [arXiv:1312.1308]
- Accumulation of periodic points for local uniformly quasiregular mappings (with Yûsuke Okuyama). In
*RIMS Kôkyûroku Bessatsu B43, 2013.*[arXiv:1306.3298]
- Slow mappings of finite distortion (with Jani Onninen).
*Math. Ann. 354 (2)*, 2012. PDF
- Quasiregularly elliptic link complements (with Kai Rajala).
*Geom. Dedicata 154 (1)*, 2011. PDF - Quasiconformal extension fields (with Kai Rajala).
*Calc. Var. Partial Differential Equations 42(1-2)*, 2011. [arXiv:1006.2259] PDF
- Mappings of bounded mean distortion and cohomology.
*Geom. Funct. Anal. 20(1)*, 2010. PDF
- Quasiconformal frames (with Juha Heinonen and Kai Rajala).
*Arch. Rat. Mech. Anal. 196(3)*, 2010. PDF
- Sharp exponential integrability for traces of monotone Sobolev functions (with Pietro Poggi-Corradini and Kai Rajala).
*Nagoya Math. Jour. 192*, 2009. [arXiv:math.AP/072332]
- Slow quasiregular mappings and universal coverings.
*Duke Math. J. 141(2)*, 2008. - p-Laplace operator, quasiregular mappings, and Picard-type theorems (with Ilkka Holopainen). In
*Quasiconformal Mappings and their Applications*, 2007, pp. 117-150. PS PDF
- Quasiregular mappings from a punctured ball into compact manifolds.
*Conform. Geom. Dyn. 10,*2006.
- A big Picard theorem for quasiregular mappings into manifolds with many ends (with Ilkka Holopainen).
*Proc. Amer. Math. Soc. 133,*2005.
- Mappings of finite distortion: Global homeomorphism theorem (with Ilkka Holopainen).
*Ann. Acad. Sci. Fenn. Ser. A I Math. 29,*2004.
- Mappings of finite distortion and weighted parabolicity. In
*Future trends in geometric function theory*(D. Herron, eds.),*Rep. Univ. Jyväskylä Dept. Math. Stat. 92*, 2003. PS PDF
## Other- Global behavior of quasiregular mappings and mappings of finite distortion under parabolic assumptions on spaces.
*Dissertation,*University of Helsinki, 2005. PDF
- Six hours on quasiregular mappings.
*Lecture notes,*April 2014. PDF
- Erään esimerkin tarina.
*Arkhimedes*(in Finnish, to appear). PDF
## See also
Geometric analysis and PDE group in Helsinki
Quasiconformal Geometry, Analysis in Metric Spaces, and Minimal surfaces a miniconference in honor of the career of Ilkka Holopainen, University of Helsinki, Dec 8, 2023.
Geometry in May University of Helsinki, May 2-3, 2017.
Quasiweekend 2 - ten years after University of Helsinki, December 10-13, 2015.
A quasiconformal life: Celebration of the legacy and work of F.W.Gehring University of Helsinki, August 11-12, 2013.
Quasiconformal Mappings and Analysis on Metric Spaces |