Solving Yamabe Problem by An Iterative Method

Jie Xu

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arXiv · 2011.14562

Solving Yamabe Problem by An Iterative Method

Jie Xu

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Abstract

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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Jie Xu. 2020-11-30. Solving Yamabe Problem by An Iterative Method. https://arxiv.org/abs/2011.14562

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