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

TL;DR

This paper provides moment estimates for the invariant measure of a stochastic PDE modeling curve shortening flow, demonstrating polynomial stability and maximal dissipativity of the associated operator.

Contribution

It introduces new moment estimates and stability results for the ergodic measure of a stochastic mean curvature flow in 1+1 dimensions.

Findings

Established moment estimates for the invariant measure

Proved polynomial stability of the Markov semigroup

Demonstrated maximal dissipativity of the Kolmogorov operator

Abstract

We establish moment estimates for the invariant measure 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 for the related Kolmogorov operator.