The parabolic Anderson model on Riemann surfaces
Antoine Dahlqvist, Joscha Diehl, Bruce K. Driver · arXiv (Cornell University) · 2017
We show well-posedness for the parabolic Anderson model on $2$-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for this equation. A central ingredient is the appropriate re-interpretation of the polynomial model, which we build up to any order.