| Abstract: |
| In this talk we will introduce some recent progress on higher order semilinear equations on hyperbolic spaces. Our results consists of the existence and symmetry of solutions to Br\`ezis-Nirenberg equations and Shr\odinger equations. Due to the complexity of hyperbolic spaces, classical variational methods such as the blow-up analysis and the mini-max theory have to be modified. Moreover, we will highlight the relation of this modification with the study of sharp Sobolev type inequalities on hyperbolic spaces. Part of these results are joint works with G. Lu. Q. Yang and Z. Wang. |
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