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

Steven Rosenberg; Jie Xu

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arXiv · 2110.14543

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

Steven Rosenberg·Jie Xu

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Abstract

We introduce an iterative scheme to solve the Yamabe equation $ - a\Delta_{g} u + S u = \lambda u^{p-1} $ on small domains $(\Omega,g)\subset {\mathbb R}^n$ 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.

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BibTeX RIS

Steven Rosenberg, Jie Xu. 2021-10-27. Solving the Yamabe Problem by an Iterative Method on a Small Riemannian Domain. https://arxiv.org/abs/2110.14543

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