Pluripotential Chern-Ricci Flows
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913812520632320 |
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| author | Dang, Quang-Tuan |
| author_facet | Dang, Quang-Tuan |
| contents | Extending a recent theory developed on compact Kähler manifolds by Guedj-Lu-Zeriahi and the author, we define and study pluripotential solutions to degenerate parabolic complex Monge-Ampère equations on compact Hermitian manifolds. Under natural assumptions on the Cauchy boundary data, we show that the pluripotential solution is semi-concave in time and continuous in space and that such a solution is unique. We also establish a partial regularity of such solutions under some extra assumptions of the densities and apply it to prove the existence and uniqueness of the weak Chern-Ricci flow on complex compact varieties with log terminal singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01150 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pluripotential Chern-Ricci Flows Dang, Quang-Tuan Differential Geometry Analysis of PDEs Complex Variables 53E30 Extending a recent theory developed on compact Kähler manifolds by Guedj-Lu-Zeriahi and the author, we define and study pluripotential solutions to degenerate parabolic complex Monge-Ampère equations on compact Hermitian manifolds. Under natural assumptions on the Cauchy boundary data, we show that the pluripotential solution is semi-concave in time and continuous in space and that such a solution is unique. We also establish a partial regularity of such solutions under some extra assumptions of the densities and apply it to prove the existence and uniqueness of the weak Chern-Ricci flow on complex compact varieties with log terminal singularities. |
| title | Pluripotential Chern-Ricci Flows |
| topic | Differential Geometry Analysis of PDEs Complex Variables 53E30 |
| url | https://arxiv.org/abs/2201.01150 |