A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866914427679277056 |
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| author | Hu, Jingchen |
| author_facet | Hu, Jingchen |
| contents | In this paper we establish a positive lower bound estimate for the second smallest eigenvalue of the complex Hessian of solutions to a degenerate complex Monge-Ampère equation. As a consequence, we find that in the space of Kähler potentials any two points close to each other in $C^2$ norm can be connected by a geodesic along which the associated metrics do not degenerate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13651 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials Hu, Jingchen Differential Geometry Analysis of PDEs 32W20 In this paper we establish a positive lower bound estimate for the second smallest eigenvalue of the complex Hessian of solutions to a degenerate complex Monge-Ampère equation. As a consequence, we find that in the space of Kähler potentials any two points close to each other in $C^2$ norm can be connected by a geodesic along which the associated metrics do not degenerate. |
| title | A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials |
| topic | Differential Geometry Analysis of PDEs 32W20 |
| url | https://arxiv.org/abs/2208.13651 |