2025/11/06 by Hua Qiu, Qiu, Hua, Haoran Tian +1
Mathematics · Materials Science · #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2511.04027
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 #Extr(uλ)\asympλdS/2 for the Sierpinski gasket, demonstrating that the complexity of eigenfunctions is governed by the spectral dimension dS. This behavior stands in sharp contrast to the corresponding growth law on Euclidean n-dimensional rectangles or balls. The attainment of the exponent dS/2 reflects the high symmetry of the underlying fractal. Our result reveals a distinct spectral-geometric phenomenon on singular spaces.