Solving the Yamabe Problem by an Iterative Method on a Small Riemannian Domain

Abstract

We introduce an iterative scheme to solve the Yamabe equation $ - aΔ_{g} u + S u = λu^{p-1} $ on small domains $(Ω,g)\subset {\mathbb R}^n$ equipped with a Riemannian metric $g$. Thus $g$ admits a conformal change to a constant scalar curvature metric. The proof does not use the traditional functional minimization.