%0 Journal Article %T The Yamabe flow on incomplete manifolds %A Yuanzhen Shao %J Mathematics %D 2015 %I arXiv %X This article is concerned with developing an analytic theory for second order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an Lp-framework is established by maximal regularity tools. These techniques are applied to the Yamabe flow. It is proven that the Yamabe flow admits a unique local solution within a class of incomplete initial metrics. %U http://arxiv.org/abs/1506.07018v2