| The Yamabe problem is a well-known problem in conformal geometry,while the?k-Yamabe problem is a fully nonlinear generalization of the classic Yamabe prob-lem,and its research has great value in the development of geometry and analysis.This thesis mainly deals with the eigenvalue problem of the ?2-Yamabe equation with Dirichlet boundary conditions,through applying the construction of the aux-iliary function,generalizing the previous gradient estimate of the Monge-Ampere equation and the k-Hessian equation to the ?2-Yamabe equation.Under some con-ditions,the gradient estimate of the eigenvalue problem of the ?2-Yamabe equation can be obtained. |
PDF Full Text Request