Self-similar Dirichlet form on pillow-type carpets--a short analytic construction

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Shiping Cao, Hua Qiu, Wang, Yizhou
DOI: 10.48550/arxiv.2601.10750
Cited by: 0

Abstract

We give a short, self-contained analytic proof of the existence of self-similar Dirichlet forms on pillow-type carpets, a family of infinitely ramified fractals that includes the Sierpiński carpet.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Mathematical Dynamics and Fractals advanced mathematical theories

Publication details

Journal / source
arXiv (Cornell University)
Publication date
13 January 2026
Document type
Preprint