Convergence of energy forms on Sierpinski gaskets with added rotated triangle

Abstract: We study the convergence of resistance metrics and resistance forms on a converging sequence of spaces. As an application, we study the existence and uniqueness of self-similar Dirichlet forms on Sierpinski gaskets with added rotated triangles. The fractals depend on a parameter in a continuous way. When the parameter is irrational, the fractal is not post critically finite (p.c.f.), and there are infinitely many ways that two cells intersect. In this case, we will define the Dirichlet form as a limit in some $\Gamma$-convergence sense of the Dirichlet forms on p.c.f. fractals that approximate it.