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
Hauptverfasser: Pham, Duc Thoan, Hoang, Thu Thuy, Nguyen, Thu Thuy, Vu, Thi Thuy
Format: Artikel
Sprache:Englisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2026
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
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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
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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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