6 papers
Unveiling topology in imaging problems via quasi-isometry and persistent homology
Elli Karvonen, Matti Lassas, Pekka Pankka
We show that the topological structures, such as loops, voids, and higher-dimensional holes of unknown objects (of flow of an object in space-time) can be recovered from noisy and…
On Lakes of Wada
Pekka Pankka, Jang-Mei Wu
There exist Lakes of Wada in which are quasiconformally equivalent to a Euclidean ball and are John domains.
Rigidity and quasisymmetric uniformization of Thurston-type maps
Zhiqiang Li, Pekka Pankka, Hanyun Zheng
We prove the No Invariant Line Fields conjecture for a class of generalized postcritically-finite branched covers on higher-dimensional Riemannian manifolds. Moreover, we establish…
The Heinonen-Semmes problems after thirty years
Guy C. David, Pekka Pankka, Jeremy T. Tyson
We survey the current status of the questions posed by Juha Heinonen and Stephen Semmes in `Thirty-three yes or no questions about mappings, measures, and metrics' (Conformal Geome…
Nodal resolution of quasiregular curves via bubble trees
Pekka Pankka, Jonathan Pim
We prove a version of Gromov's compactness theorem for quasiregular curves into calibrated manifolds with bounded geometry. In our main theorem, given an -dimensional calibratio…
Liouville's theorem in calibrated geometries
Toni Ikonen, Pekka Pankka
We consider the following extension of the classical Liouville theorem: A calibration , where , has the Liouville property if a Sobolev mapp…