https://neckpinch.com/authors/nils-dabrock/New arXiv papers by Nils Dabrock, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1903.04785/arxiv:1903.04785Tue, 12 Mar 2019 00:00:00 GMTNils Dabrock, Martina Hofmanová, Matthias Röger — We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. We establish existence of martingale solutions which are strong in the PDE sense and study their large-time behavior. Our analysis is based on a viscous approximation and new global bounds, namely, an L^(∞)_(ω,x,t) estimate for the gradient and an L²_(ω,x,t) bound for the Hessian. The proof makes essential use of the delicate interplay between the deterministic mean curvature part and the stochastic perturbation, which permits to show that certain gradient-dependent energies are supermartingales. Our energy bounds in particular imply that solutions become asymptotically spatially homogeneous and approach a Brownian motion perturbed by a random constant.Mean curvature flowHomogeneous spaces