Balanced metrics for extremal Kähler metrics and Fano manifolds
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arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911271949959168 |
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| author | Hashimoto, Yoshinori |
| author_facet | Hashimoto, Yoshinori |
| contents | The first three sections of this paper are a survey of the author's work on balanced metrics and stability notions in algebraic geometry. The last section is devoted to proving the well-known result that a geodesically convex function on a complete Riemannian manifold admits a critical point if and only if its asymptotic slope at infinity is positive, where we present a proof which relies only on the Hopf--Rinow theorem and extends to locally compact complete length metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11612 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Balanced metrics for extremal Kähler metrics and Fano manifolds Hashimoto, Yoshinori Differential Geometry Algebraic Geometry Complex Variables 53C55 (Primary), 32Q26 (Secondary) The first three sections of this paper are a survey of the author's work on balanced metrics and stability notions in algebraic geometry. The last section is devoted to proving the well-known result that a geodesically convex function on a complete Riemannian manifold admits a critical point if and only if its asymptotic slope at infinity is positive, where we present a proof which relies only on the Hopf--Rinow theorem and extends to locally compact complete length metric spaces. |
| title | Balanced metrics for extremal Kähler metrics and Fano manifolds |
| topic | Differential Geometry Algebraic Geometry Complex Variables 53C55 (Primary), 32Q26 (Secondary) |
| url | https://arxiv.org/abs/2311.11612 |