Minimal gap in the spectrum of the Sierpinski gasket

This paper studies the size of the minimal gap between any two consecutive eigenvalues in the Dirichlet and in the Neumann spectrum of the standard Laplace operator on the Sierpinski gasket. The main result shows the remarkable fact that this minimal gap is achieved and coincides with the spectral gap. The Dirichlet case is more challenging and requires some key observations in the behavior of the dynamical system that describes the spectrum.