Title: Generalized Aubin Metrics and Cohomogeneity One K\"ahler Conic Metrics with Constant Scalar Curvature

Zhuang-dan Daniel Guan (UCR)

Abstract: In this talk we shall explain the approach of using generalized Aubin metrics for searching the K\"ahler metrics with constant scalar curvatures, which is a generalization of continuity method for finding K\"ahler-Einstein metrics. We first defind the generalized Aubin metrics and then we deal with type II cohomogeneity one case. To make the explanation simpler, we forcus on the special example of the compact manifolds obtained by blowup the diagonal of the product of two copies of projective spaces. Because of the limit of times, we just set up the equations, which also show why the Harnack inequalities, the blowup analysis and the partial Futaki invariants work.