9 papers
Cartesian products of SierpiÅski carpets do not attain their conformal dimension
Riku Anttila, Sylvester Eriksson-Bique
It is a long-standing open question to determine whether the SierpiÅski carpet attains its conformal dimension or not. While this problem remains unresolved, we prove that Cartesi…
Uniqueness of sign-changing solutions to Trudinger's equation
Riku Anttila, Peter Lindqvist, Mikko Parviainen
We establish uniqueness for sign-changing solutions to Trudinger's parabolic equation with time dependent Dirichlet boundary data.
Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Lassi Rainio
A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfor…
The Combinatorial Loewner Property and super-multiplicativity inequalities for symmetric self-similar metric spaces
Riku Anttila, Sylvester Eriksson-Bique
This paper introduces a general construction of self-similar metric spaces as limits of discrete graphs. Our framework produces many classical examples, such as the SierpiÅski car…
An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces
Riku Anttila
In this work, we establish a new characterization of sub-Gaussian heat kernel estimates for strongly local regular Dirichlet forms on metric measure spaces. Our formulation is base…
Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains
Riku Anttila
We prove that sub-Gaussian heat kernel estimates are inherited from a diffusion process on the ambient space to the reflected diffusion process on a subset which is an inner unifor…