Geometric Analysis and Topology Seminar

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Higher order estimates for complex Monge-Ampere equations with small fiber size

Speaker: Valentino Tosatti, NYU Courant

Location: Warren Weaver Hall 512

Date: Friday, September 23, 2022, 11 a.m.

Synopsis:

The problem of studying the collapsing behavior of Ricci-flat Kahler metric on fibered Calabi-Yau manifolds as the fiber size shrinks translates into obtaining uniform estimates for a family of degenerating complex Monge-Ampere equations. I will describe joint work with H.J. Hein where we prove a priori C^k estimates for all k for the solution (away from the singular fibers), as a consequence of an asymptotic expansion in the fiber size, where each additional term of the expansion arises as the obstruction to proving a uniform bound on one additional derivative of the remainder.