13 papers
Walk-on-Cubes Monte Carlo Simulation for nonisotropic fractional Laplace, Helmholtz, and Yukawa equations
Antti Rasila, Tommi Sottinen, Yaotong Yuan
We study the nonisotropic fractional analogs of Laplace, Helmholtz and Yukawa equations. We provide a Duffin correspondence for the Yukawa equation and a Feynman--Kac reconstructio…
Isoperimetric-type inequalities for pluriharmonic functions on the polydisc
Suman Das, Antti Rasila, Jian-Feng Zhu
We prove isoperimetric-type inequalities for complex-valued pluriharmonic functions in the unit polydisc . Denote by and $b^p_{…
Shortest paths in planar domains with hyperbolic type metrics
Shuliang Gao, Anni Hakanen, Antti Rasila +1
We study planar domains equipped with a hyperbolic type metric and approximate geodesics that join two points and their lengths. We present an algorithm that enable…
Harmonic K-quasiconformal Koebe functions: construction and application to Pavlovic's problem
Zhi-Gang Wang, Xiao-Yuan Wang, Antti Rasila +1
We first construct the harmonic K-quasiconformal Koebe functions, filling a long-standing foundational gap in geometric function theory. This construction provides a unified parame…
On Koebe-type functions for harmonic quasiconformal mappings
Zhi-Gang Wang, Jia-Le Qiu, Antti Rasila
This paper studies a class of Koebe-type harmonic quasiconformal functions. It is motivated by the shear construction of Clunie and Sheil-Small [Ann. Acad. Sci. Fenn. Ser. A I Math…
Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem
Suman Das, Jie Huang, Antti Rasila
Let , , be the class of normalized -quasiconformal harmonic mappings in the unit disk. We obtain Baernstein type extremal results for the analytic an…