3 papers
math.FA2026
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.FA2025
BGD domains in p.c.f. self-similar sets II: spectral asymptotics for Laplacians
Qingsong Gu, Hua Qiu
Let be a p.c.f. self-similar set equipped with a strongly recurrent Dirichlet form. Under a homogeneity assumption, for an open set whose boundary i…
math.FA2024
BGD domains in p.c.f. self-similar sets I: boundary value problems for harmonic functions
Qingsong Gu, Hua Qiu
We study the boundary value problems for harmonic functions on open connected subsets of post-critically finite (p.c.f.) self-similar sets, on which the Laplacian is defined throug…