Universal Inequalities For Eigenvalues Of The Buckling Problem On A Class Of Submanifolds

Eigenvalues peoblem of Riemannian manifolds is an important subject on differ-ential geometry and geometric analysis. It is also a hot issue and has been studied extensively by mathematicians at domestic and abroad. The thesis is mainly to study universal inequalities for eigenvalues of the Buckling problem in a certain manifold.In the first part, we briefly introduce the background of eigenvalues, the achieve-ment of eigenvalues and the content of this thesis.In the second part, we mainly introduce some known knowledge related eigenval-ues, which includs basic definition, properties, theorems, an important conclusion from the Rayleigh-Ritz inequality and some basic results.The third part is the main content. We extend universal inequalities for eigenvalues of the Buckling problem in a sphere to a certain manifold. Then, we give the main conclusion and proof of universal inequalities for eigenvalues of the Buckling problem in such manifolds.