On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications
UDC 514.7 We establish the second main theorems for meromorphic mappings of complete Kähler manifolds into complex projective spaces with hyperplanes in the general position. This is a continuation of the works by Atsuji [J. Math. Soc. Japan, 60, № 2, 471–493 (2008)] and Dong [J. Inst. Math. Juss...
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| Datum: | 2026 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8785 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513283769892864 |
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| author | Pham, Duc Thoan Hoang, Thu Thuy Nguyen, Thu Thuy Vu, Thi Thuy Pham, Duc Thoan Hoang, Thu Thuy Nguyen, Thu Thuy Vu, Thi Thuy |
| author_facet | Pham, Duc Thoan Hoang, Thu Thuy Nguyen, Thu Thuy Vu, Thi Thuy Pham, Duc Thoan Hoang, Thu Thuy Nguyen, Thu Thuy Vu, Thi Thuy |
| author_sort | Pham, Duc Thoan |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:33:37Z |
| description | UDC 514.7
We establish the second main theorems for meromorphic mappings of complete Kähler manifolds into complex projective spaces with hyperplanes in the general position. This is a continuation of the works by Atsuji [J. Math. Soc. Japan, 60, № 2, 471–493 (2008)] and Dong [J. Inst. Math. Jussieu, 1–29 (2022)]. We extend the results of these works to targets of higher dimension. As an application, we show that every meromorphic mapping of a complete Kähler manifold of nonpositive Ricci curvature and maximal volume growth into complex projective spaces with small growth, as compared to a half of the traceless Ricci curvature of the manifold, must be constant. |
| doi_str_mv | 10.3842/umzh.v77i8.8785 |
| first_indexed | 2026-03-24T03:42:13Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8785 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:42:13Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-87852026-03-21T13:33:37Z On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications Pham, Duc Thoan Hoang, Thu Thuy Nguyen, Thu Thuy Vu, Thi Thuy Pham, Duc Thoan Hoang, Thu Thuy Nguyen, Thu Thuy Vu, Thi Thuy K\ Primary 32H30, 32A22; Secondary 30D35 UDC 514.7 We establish the second main theorems for meromorphic mappings of complete Kähler manifolds into complex projective spaces with hyperplanes in the general position. This is a continuation of the works by Atsuji [J. Math. Soc. Japan, 60, № 2, 471–493 (2008)] and Dong [J. Inst. Math. Jussieu, 1–29 (2022)]. We extend the results of these works to targets of higher dimension. As an application, we show that every meromorphic mapping of a complete Kähler manifold of nonpositive Ricci curvature and maximal volume growth into complex projective spaces with small growth, as compared to a half of the traceless Ricci curvature of the manifold, must be constant. УДК 514.7 Про деякі другі основні теореми для мероморфних відображень повних келерових многовидів із гіперплощинами та їхні застосування Встановлено другі основні теореми для мероморфних відображень повних келерових многовидів у комплексні проєктивні простори з гіперплощинами загального положення. Ця робота є продовженням робіт Ацуї [J. Math. Soc. Japan, 60, № 2, 471–493 (2008)] і Донга [J. Inst. Math. Jussieu, 1–29 (2022)], результати яких у цій статті розширено на цілі простори вищої розмірності. Як застосування показано, що будь-яке мероморфне відображення повного келерового многовиду з недодатною кривиною Річчі та максимальним зростанням об’єму у комплексні проєктивні простори з малим зростанням, порівняно з половиною безслідної кривини Річчі многовиду, має бути сталою функцією. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8785 10.3842/umzh.v77i8.8785 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 8 (2025); 538–539 Український математичний журнал; Том 77 № 8 (2025); 538–539 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8785/10555 Copyright (c) 2025 Duc Thoan Pham, Thu Thuy Nguyen, Thi Thuy Vu |
| spellingShingle | Pham, Duc Thoan Hoang, Thu Thuy Nguyen, Thu Thuy Vu, Thi Thuy Pham, Duc Thoan Hoang, Thu Thuy Nguyen, Thu Thuy Vu, Thi Thuy On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications |
| title | On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications |
| title_alt | On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications |
| title_full | On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications |
| title_fullStr | On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications |
| title_full_unstemmed | On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications |
| title_short | On some second main theorems for meromorphic mappings of complete Kähler manifolds with hyperplanes and their applications |
| title_sort | on some second main theorems for meromorphic mappings of complete kähler manifolds with hyperplanes and their applications |
| topic_facet | K\ Primary 32H30 32A22; Secondary 30D35 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8785 |
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