Solving Yamabe Problem by An Iterative Method

Abstract

We introduce an iterative scheme to prove the Yamabe problem $-a{\Delta }_{g}u+Su=\lambda u^{p-1}$, 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 $n⩾3$ in a uniform argument, beyonds the traditional analysis with respect to the minimization of functionals.

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