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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