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A complete complex hypersurface in the ball of ▫$\mathbb{C}^N$▫Globevnik, Josip, 1945-Leta 1977 je P. Yang vprašal, če obstajajo kompletne imergirane kompleksne podmnogoterosti ▫$\varphi \colon M^k \to \mathbb{C}^N$▫, ki so omejene. Pozitiven odgovor je znan za holomorfne krivulje ... ▫$(k=1)$▫ in delni odgovori so znani v primeru, ko je ▫$k>1$▫. Glavni rezultat članka je konstrukcija holomorfne funkcije na odprti enotski krogli ▫$\mathbb{B}_N$▫ prostora ▫$\mathbb{C}^N$▫, katere realni del je neomejen na vsaki poti v ▫$\mathbb{B}_N$▫, ki ima končno dolžino in se konča na ▫$b\mathbb{B}_N$▫. Posledica tega je obstoj kompletne, zaprte kompleksne hiperploskve v ▫$\mathbb{B}_N$▫. To da pritrdilni odgovor na Yangovo vprašanje v vseh dimenzijah ▫$k$▫, ▫$N$▫, ▫$1 \le k < N$▫, saj ima za posledico obstoj kompletne kompleksne mnogoterosti, vložene v kroglo s pravo preslikavo.Source: Annals of mathematics. - ISSN 0003-486X (Vol. 182, iss. 3, 2015, str. 1067-1091)Type of material - article, component partPublish date - 2015Language - englishCOBISS.SI-ID - 17459545
Author
Globevnik, Josip, 1945-
Topics
matematika |
kompleksna analiza |
omejene kompleksne holomorfne vložitve |
kompletne kompleksne mnogoterosti |
kompletne holomorfne imerzije |
mathematics |
complex analysis |
bounded complete holomorphic embeddings |
complete complex manifolds |
complete holomorphic immersions
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Globevnik, Josip, 1945- | 02301 |
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