Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity
Abstract
We show that on every non- $G_2$ complex symmetric space of rank two, there are complete Calabi-Yau metrics of Euclidean volume growth with prescribed horospherical singular tangent cone at infinity, providing the first examples of affine Calabi-Yau smoothings of singular and irregular tangent cone. As a corollary, we obtain infinitely many examples of Calabi-Yau manifolds degenerating to the tangent cone in a single step, supporting a recent conjecture by Sun-Zhang, which was only proved when the tangent cone at infinity has only an isolated singularity.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Advanced Algebra and Geometry
Publication details
- Journal / source
- Journal of Differential Geometry
- Publisher
- International Press of Boston
- Volume
- 133
- Issue
- 3
- Pages
- 373-441
- Publication date
- 28 May 2026
- Language
- EN