Holomorphic Rigidity of CR Maps Between Levi-Degenerate Hypersurfaces
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| Natura: | Recurso digital |
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2025
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| _version_ | 1866901772648316928 |
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| author | Revista, Zen MATH, 10 |
| author_facet | Revista, Zen MATH, 10 |
| contents | This paper explores the intricate phenomenon of holomorphic rigidity for Cauchy-Riemann (CR) maps between Levi-degenerate hypersurfaces in complex spaces. While the theory of CR maps between Levi-non-degenerate hypersurfaces is well-established, the Levi-degenerate case presents significant challenges due to the vanishing of the Levi form in certain directions, leading to a richer and more complex geometric structure. We delve into how the higher-order geometric invariants of Levi-degenerate hypersurfaces influence the local and global behavior of CR maps. The study synthesizes results concerning the regularity, extension, and rigidity properties of such mappings, drawing connections to invariant theory and generalizations of Huang's Lemma. Specifically, we investigate conditions under which CR maps are forced to be locally biholomorphic, globally proper, or adhere to specific algebraic forms. The implications for the understanding of proper holomorphic maps between bounded symmetric domains with Levi-degenerate boundaries are also discussed, highlighting the role of 2-nondegeneracy and higher-order tensors. This work contributes to a deeper understanding of the interplay between complex geometry and the analysis of mappings in the presence of Levi degeneracy. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17713294 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Holomorphic Rigidity of CR Maps Between Levi-Degenerate Hypersurfaces Revista, Zen MATH, 10 This paper explores the intricate phenomenon of holomorphic rigidity for Cauchy-Riemann (CR) maps between Levi-degenerate hypersurfaces in complex spaces. While the theory of CR maps between Levi-non-degenerate hypersurfaces is well-established, the Levi-degenerate case presents significant challenges due to the vanishing of the Levi form in certain directions, leading to a richer and more complex geometric structure. We delve into how the higher-order geometric invariants of Levi-degenerate hypersurfaces influence the local and global behavior of CR maps. The study synthesizes results concerning the regularity, extension, and rigidity properties of such mappings, drawing connections to invariant theory and generalizations of Huang's Lemma. Specifically, we investigate conditions under which CR maps are forced to be locally biholomorphic, globally proper, or adhere to specific algebraic forms. The implications for the understanding of proper holomorphic maps between bounded symmetric domains with Levi-degenerate boundaries are also discussed, highlighting the role of 2-nondegeneracy and higher-order tensors. This work contributes to a deeper understanding of the interplay between complex geometry and the analysis of mappings in the presence of Levi degeneracy. |
| title | Holomorphic Rigidity of CR Maps Between Levi-Degenerate Hypersurfaces |
| url | https://doi.org/10.5281/zenodo.17713294 |