Smooth asymptotics for collapsing Calabi-Yau metrics

Talk by Hans-Joachim Hein (Münster) on occasion of the 70th birthday
of Prof. Werner Ballmann

Yau's solution of the Calabi conjecture provided the first nontrivial examples of Ricci-flat Riemannian metrics on compact manifolds. Attempts to understand the degeneration patterns of these metrics in families have revealed many remarkable phenomena over the years. I will review some aspects of this story and present recent joint work with Valentino Tosatti where we obtain a complete asymptotic expansion (locally uniformly away from the singular fibers) of Calabi-Yau metrics collapsing along a holomorphic fibration of a fixed compact Calabi-Yau manifold. This relies on a new analytic method where each additional term of the expansion arises as the obstruction to proving a uniform bound on one additional derivative of the remainder.

The seminar is virtual via Zoom.
Contact: Stephan Stadler (stadler@mpim-bonn.mpg.de)