Uniform rigidity sequences for weak mixing diffeomorphisms on D2, A and T2

In the case of the disc D2, the annulus A=S1×[0,1] and the torus T2 we will show that if a sequence of natural numbers satisfies a certain growth rate, then there is a weak mixing diffeomorphism that is uniformly rigid with respect to that sequence. The proof is based on a quantitative version of the Anosov-Katok-method with explicitly defined conjugation maps and the constructions are done in the C∞-topology. Beyond that we can deduce a similar result in the real-analytic topology in the case of T2.