Topological invariants and Holomorphic Mappings
Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold are investigated. The invariants are monotonic under holomorp...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.336/ |
| _version_ | 1797651480657788928 |
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| author | Greene, Robert E. Kim, Kang-Tae Shcherbina, Nikolay V. |
| author_facet | Greene, Robert E. Kim, Kang-Tae Shcherbina, Nikolay V. |
| author_sort | Greene, Robert E. |
| collection | DOAJ |
| description | Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold are investigated. The invariants are monotonic under holomorphic mappings and strictly monotonic under certain circumstances. Applications to holomorphic maps of annular regions in $\mathbb{C}$ and tubular neighborhoods of compact totally real submanifolds in general in $\mathbb{C}^n$, $n \ge 2$, are given. The contractibility of a hyperbolic domain with contracting holomorphic mapping is explained. |
| first_indexed | 2024-03-11T16:16:24Z |
| format | Article |
| id | doaj.art-88ef8a1d940d45f5a94ebdf163fe82ee |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:24Z |
| publishDate | 2022-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-88ef8a1d940d45f5a94ebdf163fe82ee2023-10-24T14:19:39ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692022-09-01360G882984410.5802/crmath.33610.5802/crmath.336Topological invariants and Holomorphic MappingsGreene, Robert E.0Kim, Kang-Tae1Shcherbina, Nikolay V.2Department of Mathematics, University of California, Los Angeles, CA 90095 U.S.A.Department of Mathematics, Pohang University of Science and Technology, Pohang City 37673 South KoreaDepartment of Mathematics, University of Wuppertal, 42119 Wuppertal, GermanyInvariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold are investigated. The invariants are monotonic under holomorphic mappings and strictly monotonic under certain circumstances. Applications to holomorphic maps of annular regions in $\mathbb{C}$ and tubular neighborhoods of compact totally real submanifolds in general in $\mathbb{C}^n$, $n \ge 2$, are given. The contractibility of a hyperbolic domain with contracting holomorphic mapping is explained.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.336/ |
| spellingShingle | Greene, Robert E. Kim, Kang-Tae Shcherbina, Nikolay V. Topological invariants and Holomorphic Mappings Comptes Rendus. Mathématique |
| title | Topological invariants and Holomorphic Mappings |
| title_full | Topological invariants and Holomorphic Mappings |
| title_fullStr | Topological invariants and Holomorphic Mappings |
| title_full_unstemmed | Topological invariants and Holomorphic Mappings |
| title_short | Topological invariants and Holomorphic Mappings |
| title_sort | topological invariants and holomorphic mappings |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.336/ |
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