Auxiliary Monge-Ampère Equations in Orbifold Setting -- a Mean-Value Inequality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910397392486400 |
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| author | Scheffler, Johannes |
| author_facet | Scheffler, Johannes |
| contents | In this note, we generalize a mean-value inequality of Guo-Phong-Sturm to the setting of a compact Kähler orbifold. This shows that their reasoning is insensitive to quotient singularities. As we aim for a self-contained exposition, we generalize some fundamental results, namely the $α$-invariant estimate by Hörmander and Tian, an approximation result for the psh-envelope of a $(1,1)$-form in a Kähler class by Berman and an $L^\infty$ estimate for this envelope by Guo-Phong-Tong-Wang. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_02812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Auxiliary Monge-Ampère Equations in Orbifold Setting -- a Mean-Value Inequality Scheffler, Johannes Differential Geometry Complex Variables In this note, we generalize a mean-value inequality of Guo-Phong-Sturm to the setting of a compact Kähler orbifold. This shows that their reasoning is insensitive to quotient singularities. As we aim for a self-contained exposition, we generalize some fundamental results, namely the $α$-invariant estimate by Hörmander and Tian, an approximation result for the psh-envelope of a $(1,1)$-form in a Kähler class by Berman and an $L^\infty$ estimate for this envelope by Guo-Phong-Tong-Wang. |
| title | Auxiliary Monge-Ampère Equations in Orbifold Setting -- a Mean-Value Inequality |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2404.02812 |