3 papers
math.FA2025
The growth of eigenfunction extrema on p.c.f. fractals
Hua Qiu, Haoran Tian
This paper studies the growth of local extrema of Laplacian eigenfunctions on post-critically finite (p.c.f.) fractals. We establish the sharp two-sided estimate $\#\mathrm{Extr}(u…
math.FA2017
Restrictions of Laplacian eigenfunctions to edges in the Sierpinski gasket
Hua Qiu, Haoran Tian
In this paper, we study the restrictions of both the harmonic functions and the eigenfunctions of the symmetric Laplacian to edges of pre-gaskets contained in the Sierpinski gasket…
math.FA2016
The Laplacian on the unit square in a self-similar manner
Hua Qiu, Haoran Tian
In this paper, we show how to construct the standard Laplacian on the unit square in a self-similar manner. We rewrite the familiar mean value property of planar harmonic functions…