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

Abstract

We introduce an iterative scheme to solve the Yamabe equation $-a\hat{I}{”}_{g}u+Su=\hat{I}»u^{p-1}$ on small domains $(\hat{I}\text{c◯},g)\subset {\mathbb{R}}^n$ 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.