Tian's properness conjectures: an introduction to Kahler geometry
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866913581271875584 |
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| author | Rubinstein, Yanir A. |
| author_facet | Rubinstein, Yanir A. |
| contents | This manuscript served as lecture notes for a mini-course in the 2016 Southern California Geometric Analysis Seminar Winter School. The goal is to give a quick introduction to Kahler geometry by describing the recent resolution of Tian's three influential properness conjectures in joint work with T. Darvas. These results---inspired by and analogous to work on the Yamabe problem in conformal geometry---give an analytic characterization for the existence of Kahler--Einstein metrics and other important canonical metrics in complex geometry, as well as strong borderline Sobolev type inequalities referred to as the (strong) Moser--Trudinger inequalities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1807_00928 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Tian's properness conjectures: an introduction to Kahler geometry Rubinstein, Yanir A. Differential Geometry Analysis of PDEs Complex Variables 32Q20, 58E11 (primary), 53C25, 53C55, 14J50, 32W20, 32U05 (secondary) This manuscript served as lecture notes for a mini-course in the 2016 Southern California Geometric Analysis Seminar Winter School. The goal is to give a quick introduction to Kahler geometry by describing the recent resolution of Tian's three influential properness conjectures in joint work with T. Darvas. These results---inspired by and analogous to work on the Yamabe problem in conformal geometry---give an analytic characterization for the existence of Kahler--Einstein metrics and other important canonical metrics in complex geometry, as well as strong borderline Sobolev type inequalities referred to as the (strong) Moser--Trudinger inequalities. |
| title | Tian's properness conjectures: an introduction to Kahler geometry |
| topic | Differential Geometry Analysis of PDEs Complex Variables 32Q20, 58E11 (primary), 53C25, 53C55, 14J50, 32W20, 32U05 (secondary) |
| url | https://arxiv.org/abs/1807.00928 |