Freid Tong, Harvard University
"On complete Calabi-Yau metrics and a free-boundary Monge-Ampere equation"
Calabi-Yau metrics are Ricci-flat, Kähler metrics, and they are central objects in Kähler geometry. The existence problem for Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture. The situation in the non-compact setting is much more delicate, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. A major difficulty lies in the lack of suitable model metrics that model the asymptotics of the Calabi-Yau metric at spatial infinity. In this talk, I will give an introduction to this subject and discuss some joint work with T. Collins and S.-T. Yau, on a new relationship between non-compact Calabi-Yau metrics and a free-boundary Monge-Ampere equation, which allows us to resolve this problem of the lack of model metrics.
MC 5501