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Smooth asymptotics for collapsing Calabi-Yau metrics

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Hans-Joachim Hein
Universität Münster
Thu, 15/04/2021 - 15:00 - 16:30
Parent event: 

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 (

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