Convexity of the K-energy and Uniqueness of Extremal metrics -- An Expository Introduction
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909887927156736 |
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| author | Berman, Robert J. Berndtsson, Bo |
| author_facet | Berman, Robert J. Berndtsson, Bo |
| contents | This article is an expository introduction to our paper Convexity of the K-energy and Uniqueness of Extremal metrics. We present the main ideas behind the proof that Mabuchi's K-energy functional is convex along weak geodesics in the space of Kahler potentials and explain how this leads to the uniqueness of constant scalar curvature Kahler metrics and extremal metrics up to automorphisms. The emphasis is on the conceptual framework and key techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03544 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convexity of the K-energy and Uniqueness of Extremal metrics -- An Expository Introduction Berman, Robert J. Berndtsson, Bo Differential Geometry Complex Variables This article is an expository introduction to our paper Convexity of the K-energy and Uniqueness of Extremal metrics. We present the main ideas behind the proof that Mabuchi's K-energy functional is convex along weak geodesics in the space of Kahler potentials and explain how this leads to the uniqueness of constant scalar curvature Kahler metrics and extremal metrics up to automorphisms. The emphasis is on the conceptual framework and key techniques. |
| title | Convexity of the K-energy and Uniqueness of Extremal metrics -- An Expository Introduction |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2511.03544 |