Stochastic heat equations with values in a Riemannian manifold Röckner, Michael Röckner Michael Wu, Bo Wu Bo Zhu, Rongchan Zhu Rongchan Zhu, Xiangchan Zhu Xiangchan The main result of this note is the existence of martingale solutions to the stochastic heat equation (SHE) in a Riemannian manifold by using suitable Dirichlet forms on the corresponding path/loop space. Moreover, we present some characterizations of the lower bound of the Ricci curvature by functional inequalities of various associated Dirichlet forms. 29 1 205-213 205-213 European Mathematical Soc 2018