UC Berkeley

Aubin and Yau proved that every compact Kahler manifold with negative first Chern class admits a unique metric g such that Ric(g) =-g. Understanding how families of these metrics degenerate gives insight into their geometry and is important for understanding the compactification of the moduli space of negative Kahler-Einstein metrics. I study a special class of such families in complex dimension two. Following the work of Sun and Zhang in the Calabi-Yau case, I construct a Kahler-Einstein neck region interpolating between canonical metrics on components of the central fiber. This provides a model for the limiting geometry of metrics in the family.