Zalcman's lemma, Pinchuk's rescaling method, and Catlin's estimates revisited
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914985594060800 |
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| author | Berteloot, François |
| author_facet | Berteloot, François |
| contents | We present a renormalization lemma for certain maps defined on the unit disc of C and taking values in some metric space. We show that the classical renormalization lemmas of Zalcman and Miniowitz can be deduced from our lemma. We also use it to establish a general normality statement for the Pinchuk's scaling method in C^2 and, incidentally, reprove the Catlin's estimates for the Kobayashi metric in finite type domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zalcman's lemma, Pinchuk's rescaling method, and Catlin's estimates revisited Berteloot, François Complex Variables We present a renormalization lemma for certain maps defined on the unit disc of C and taking values in some metric space. We show that the classical renormalization lemmas of Zalcman and Miniowitz can be deduced from our lemma. We also use it to establish a general normality statement for the Pinchuk's scaling method in C^2 and, incidentally, reprove the Catlin's estimates for the Kobayashi metric in finite type domains. |
| title | Zalcman's lemma, Pinchuk's rescaling method, and Catlin's estimates revisited |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2410.17633 |