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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01773 |
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| _version_ | 1866914598371721216 |
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| author | Tazoe, Itsuki |
| author_facet | Tazoe, Itsuki |
| contents | We study an asymptotic behavior of the second Chern forms of canonical metrics on a degenerating family of Kähler surfaces with the central fibre having ADE-singularities. We investigate a function on the unit disc defined by fiber integrals of the forms with a smooth test function on the family. We show a lower bound of the Hölder exponent of the function at the origin. Our main results consists of two cases: one is a bound of Hölder exponent along a line for cscK-metrics, using Biquard-Rollin's a priori estimates for cscK-metrics, and the other is a bound of Hölder exponent at the origin for Ricci-flat metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On asymptotic behavior of the second Chern forms on degenerating Kähler-Einstein surfaces Tazoe, Itsuki Differential Geometry We study an asymptotic behavior of the second Chern forms of canonical metrics on a degenerating family of Kähler surfaces with the central fibre having ADE-singularities. We investigate a function on the unit disc defined by fiber integrals of the forms with a smooth test function on the family. We show a lower bound of the Hölder exponent of the function at the origin. Our main results consists of two cases: one is a bound of Hölder exponent along a line for cscK-metrics, using Biquard-Rollin's a priori estimates for cscK-metrics, and the other is a bound of Hölder exponent at the origin for Ricci-flat metrics. |
| title | On asymptotic behavior of the second Chern forms on degenerating Kähler-Einstein surfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.01773 |