Comparison Theorems for Fractional GJMS operators and the Applications

Fang Wang, Shanghai Jiaotong University
Fine Hall 314

The Fractional GJMS operators are one-parameter family of conformally invariant operators, defined by the renormalized scattering operators on the conformal infinity of Poincare-Einstein Manifolds. These operators provide a bridge to transfer the information of interior Einstein geometry to the boundary conformal geometry. In this talk, I will first introduce too types of comparison theorems for them: integral type and pointwise type. Then I will give some applications of these comparison theorems, including the estimates for interior Gromov-Bishop volume ratio and the positive mass theorem.