On the construction of non-isometric isospectral fractal drums in R3 and spectral asymptotics

We construct a pair of disjoint non-isometric isospectral fractal drums in R3, in which the boundaries have the same Minkowski dimension. We also estimate the second asymptotic term for the Dirichlet counting function and obtain the exact second term and two side sharp estimates for the remainder term of the counting function. Our result shows Weyl-Berry conjecture is not true for the case here.