The Ricci iteration towards cscK metrics
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908344454742016 |
|---|---|
| author | Zhang, Kewei |
| author_facet | Zhang, Kewei |
| contents | Motivated by the problem of finding constant scalar curvature Kähler metrics, we investigate a Ricci iteration sequence of Rubinstein that discretizes the pseudo-Calabi flow. While the long time existence of the flow is still an open question, we show that the iteration sequence does exist for all steps, along which the K-energy decreases. We further show that the iteration sequence, modulo automorphisms, converges smoothly to a constant scalar curvature Kähler metric if there is one, thus confirming a conjecture of Rubinstein from 2007 and extending results of Darvas--Rubinstein to arbitrary Kähler classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15524 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Ricci iteration towards cscK metrics Zhang, Kewei Differential Geometry Analysis of PDEs Dynamical Systems Motivated by the problem of finding constant scalar curvature Kähler metrics, we investigate a Ricci iteration sequence of Rubinstein that discretizes the pseudo-Calabi flow. While the long time existence of the flow is still an open question, we show that the iteration sequence does exist for all steps, along which the K-energy decreases. We further show that the iteration sequence, modulo automorphisms, converges smoothly to a constant scalar curvature Kähler metric if there is one, thus confirming a conjecture of Rubinstein from 2007 and extending results of Darvas--Rubinstein to arbitrary Kähler classes. |
| title | The Ricci iteration towards cscK metrics |
| topic | Differential Geometry Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2311.15524 |