Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow

Abstract

We establish moment estimates for the invariant measure μ of a stochastic partial differential equation describing motion by mean curvature flow in (1+1) dimension, leading to polynomial stability of the associated Markov semigroup. We also prove maximal dissipativity on L 1(μ) for the related Kolmogorov operator. © 2012 Springer Basel AG.