Smooth asymptotics for collapsing Calabi-Yau metrics

Hans-Joachim Hein (University of Münster)

22-Jun-2021, 17:00-18:00 (3 years ago)

Abstract: 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.

mathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( paper | slides )


Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

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Organizers: Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang
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