3 problems

Let $K$ be the Sierpiński gasket. For a nonconstant harmonic function $h$ on $K$, let $u_h=\mu_h/\mu_h(K)$ be its normalized energy measure. For nonconstant harmonic functions…

Bouleau–Hirsch energy image density conjecture. Every Dirichlet structure satisfies the energy image density property.

Energy measure singularity dichotomy. Then $\Gamma(f,f) \perp m$ for all $f \in \mathcal{F}$. The conjecture predicts singularity of every energy measure under the stated structura…