Comptes Rendus
Analyse et géométrie complexes
Topological invariants and Holomorphic Mappings
Robert E. Greene1 ; Kang-Tae Kim2  ; Nikolay V. Shcherbina3
1 Department of Mathematics, University of California, Los Angeles, CA 90095 U.S.A.
2 Department of Mathematics, Pohang University of Science and Technology, Pohang City 37673 South Korea
3 Department of Mathematics, University of Wuppertal, 42119 Wuppertal, Germany
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 829-844.

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 ℂ and tubular neighborhoods of compact totally real submanifolds in general in ℂ n , n≥2, are given. The contractibility of a hyperbolic domain with contracting holomorphic mapping is explained.

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DOI : 10.5802/crmath.336
Robert E. Greene 1 ; Kang-Tae Kim 2 ; Nikolay V. Shcherbina 3

1 Department of Mathematics, University of California, Los Angeles, CA 90095 U.S.A.
2 Department of Mathematics, Pohang University of Science and Technology, Pohang City 37673 South Korea
3 Department of Mathematics, University of Wuppertal, 42119 Wuppertal, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Topological invariants and {Holomorphic} {Mappings}},
     journal = {Comptes Rendus. Math\'ematique},
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     publisher = {Acad\'emie des sciences, Paris},
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     doi = {10.5802/crmath.336},
     language = {en},
}
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Robert E. Greene; Kang-Tae Kim; Nikolay V. Shcherbina. Topological invariants and Holomorphic Mappings. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 829-844. doi : 10.5802/crmath.336. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.336/

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