A P.C.F. Self-Similar Set with no Self-Similar Energy
arXiv:1701.07885
Abstract
A general class of finitely ramified fractals is that of P.C.F. self-similar sets. An important open problem in analysis on fractals was whether there exists a self-similar energy on every P.C.F. self-similar set. In this paper, I solve the problem, showing an example of a P.C.F. self-similar set where there exists no self-similar energy.
6 pages