Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | Kewei Zhang
| | Inviter: | | Title:
| Calabi ansatz and canonical metrics | Time & Venue:
| 2019.12.21 14:40-15:40 N226 | Abstract:
| In this I wil review a well-studied construction, initiated by Calabi, which can effectively produce various explicit examples of canonical metrics in K\"ahler geometry. The idea is to work on complex manifolds with certain symmetries so that one can reduce geometric PDEs to simple ODEs. This approach is often referred to as the Calabi ansatz in the literature, which has been studied and generalzed to different extent by many authors. We aim to further exploit this ansatz by allowing edge singularities in the construction, from which one can see some new and intriguing geometric features relating to canonical edge metrics, Sasakian geometry, Cheeger--Colding theory, K-stability and normalized volume.
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