Corpus ID: 227228702

# Solving Yamabe Problem by An Iterative Method.

@article{Xu2020SolvingYP,
title={Solving Yamabe Problem by An Iterative Method.},
author={Jie Xu},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Jie Xu
• Published 2020
• Mathematics
• arXiv: Analysis of PDEs
We introduce an iterative scheme to prove the Yamabe problem $- a\Delta_{g} u + S u = \lambda u^{p-1}$, firstly on open domain $(\Omega, g)$ with Dirichlet boundary conditions, and then on closed manifolds $(M, g)$ by local argument. It is a new proof, which solves the Yamabe problem for $n \geqslant 3$ in a uniform argument, beyonds the traditional analysis with respect to the minimization of functionals.

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