Regularity of solutions to Monge--Ampère equations on compact Hermitian manifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914425256017920 |
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| author | Dang, Quang-Tuan |
| author_facet | Dang, Quang-Tuan |
| contents | We study the stability and Hölder continuity of solutions to degenerate complex Monge--Ampère equations associated with a (non-closed) big form on compact Hermitian manifolds. We also show that the solution is globally continuous when the reference form is the pullback of a Hermitian metric. As a consequence, we establish a uniform diameter bound for the twisted Chern--Ricci flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularity of solutions to Monge--Ampère equations on compact Hermitian manifolds Dang, Quang-Tuan Differential Geometry Complex Variables 32U20 We study the stability and Hölder continuity of solutions to degenerate complex Monge--Ampère equations associated with a (non-closed) big form on compact Hermitian manifolds. We also show that the solution is globally continuous when the reference form is the pullback of a Hermitian metric. As a consequence, we establish a uniform diameter bound for the twisted Chern--Ricci flow. |
| title | Regularity of solutions to Monge--Ampère equations on compact Hermitian manifolds |
| topic | Differential Geometry Complex Variables 32U20 |
| url | https://arxiv.org/abs/2603.25520 |