Two variational problems in Kähler geometry
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917655647092736 |
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| author | Lempert, Laszlo |
| author_facet | Lempert, Laszlo |
| contents | On a Kähler manifold we consider the problems of maximizing/minimizing Monge--Ampère energy over certain subsets of the space of Kähler potentials. Under suitable assumptions we prove that solutions to these variational problems exist, are unique, and have a simple characterization. We then use the extremals to construct hermitian metrics on holomorphic vector bundles, and investigate their curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two variational problems in Kähler geometry Lempert, Laszlo Complex Variables Differential Geometry Metric Geometry 32Q15, 32U05, 32W20, 52A40, 58E40 On a Kähler manifold we consider the problems of maximizing/minimizing Monge--Ampère energy over certain subsets of the space of Kähler potentials. Under suitable assumptions we prove that solutions to these variational problems exist, are unique, and have a simple characterization. We then use the extremals to construct hermitian metrics on holomorphic vector bundles, and investigate their curvature. |
| title | Two variational problems in Kähler geometry |
| topic | Complex Variables Differential Geometry Metric Geometry 32Q15, 32U05, 32W20, 52A40, 58E40 |
| url | https://arxiv.org/abs/2405.00869 |