The Injectivity Theorem on a Non-Compact Kähler Manifold

In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold <i>X</i> with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds...

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Autor principal:	Jingcao Wu
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	non-compact Kähler manifold Hodge decomposition harmonic differential form Hilbert space Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8f38354da8f248dcbedf4ad73a52aa15
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id	oai:doaj.org-article:8f38354da8f248dcbedf4ad73a52aa15
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spelling	oai:doaj.org-article:8f38354da8f248dcbedf4ad73a52aa152021-11-25T19:07:43ZThe Injectivity Theorem on a Non-Compact Kähler Manifold10.3390/sym131122222073-8994https://doaj.org/article/8f38354da8f248dcbedf4ad73a52aa152021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2222https://doaj.org/toc/2073-8994In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold <i>X</i> with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, such as symmetric spaces, bounded symmetric domains in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula>, hyperconvex bounded domains, and so on.Jingcao WuMDPI AGarticlenon-compact Kähler manifoldHodge decompositionharmonic differential formHilbert spaceMathematicsQA1-939ENSymmetry, Vol 13, Iss 2222, p 2222 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	non-compact Kähler manifold Hodge decomposition harmonic differential form Hilbert space Mathematics QA1-939
spellingShingle	non-compact Kähler manifold Hodge decomposition harmonic differential form Hilbert space Mathematics QA1-939 Jingcao Wu The Injectivity Theorem on a Non-Compact Kähler Manifold
description	In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold <i>X</i> with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, such as symmetric spaces, bounded symmetric domains in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula>, hyperconvex bounded domains, and so on.
format	article
author	Jingcao Wu
author_facet	Jingcao Wu
author_sort	Jingcao Wu
title	The Injectivity Theorem on a Non-Compact Kähler Manifold
title_short	The Injectivity Theorem on a Non-Compact Kähler Manifold
title_full	The Injectivity Theorem on a Non-Compact Kähler Manifold
title_fullStr	The Injectivity Theorem on a Non-Compact Kähler Manifold
title_full_unstemmed	The Injectivity Theorem on a Non-Compact Kähler Manifold
title_sort	injectivity theorem on a non-compact kähler manifold
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/8f38354da8f248dcbedf4ad73a52aa15
work_keys_str_mv	AT jingcaowu theinjectivitytheoremonanoncompactkahlermanifold AT jingcaowu injectivitytheoremonanoncompactkahlermanifold
_version_	1718410289985093632

The Injectivity Theorem on a Non-Compact Kähler Manifold

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