埃尔米特流形上的光滑函数的有界性
The Boundedness of Smooth Functions on Hermite Manifolds
DOI: 10.12677/AAM.2023.1211468, PDF,   
作者: 闫 烁：浙江师范大学数学科学学院，浙江 金华
关键词: 埃尔米特流形；复拉普拉斯算子；施瓦茨引理；Hermitian Manifolds； Complex Laplacian Operator； Schwarz’s Lemma
摘要: 本文研究完备埃尔米特流形上的光滑函数的有界性质。特别地，如果完备埃尔米特流形上的一个正的光滑函数的复拉普拉斯满足一个基本不等式，那么可以证明该函数有有限的上界值。
Abstract: In this paper, we study the boundedness of smooth functions on complete Hermitian manifolds. If the complex Laplacian of a positive smooth function on a complete Hermitian manifold satisfies a fundamental inequality, we can prove that the function has a finite upper bound.
文章引用：闫烁. 埃尔米特流形上的光滑函数的有界性[J]. 应用数学进展, 2023, 12(11): 4755-4760. https://doi.org/10.12677/AAM.2023.1211468

参考文献

[1] Yau, S.T. (1975) Harmonic Functions on Complete Riemannian Manifolds. Communications on Pure and Applied Mathematics, 28, 201-228. [Google Scholar] [CrossRef] 
[2] Yau, S.T. (1978) A General Schwarz Lemma for Kähler Manifolds. American Journal of Mathematics, 100, 197-203. [Google Scholar] [CrossRef] 
[3] Yang, X.K. and Zheng, F.Y. (2019) On Real Bisectional Curvature for Hermitian Manifolds. Transactions of the American Mathematical Society, 371, 2703-2718. [Google Scholar] [CrossRef] 
[4] Ni, L. (2019) General Schwarz Lemmata and Their Applications. International Journal of Mathematics, 13, Article 1940007. [Google Scholar] [CrossRef] 
[5] Ni, L. (2021) Liouville Theorems and a Schwarz Lemma for Holomorphic Mappings between Kähler Manifolds. Communications on Pure and Applied Mathematics, 74, 1100-1126. [Google Scholar] [CrossRef] 
[6] 白正国, 沈一兵, 水乃翔, 郭孝英. 黎曼几何初步[M]. 北京: 高等教育出版社, 2004.
[7] Zheng, F.Y. (2000) Complex Differential Geometry (AMS/IP Studies in Advanced Mathematics, 18). 1st Edition, International Press, Boston.
[8] Lu, Y.C. (1968) Holomorphic Mappings of Complex Manifolds. Journal of Differential Geometry, 2, 299-312. [Google Scholar] [CrossRef] 

为你推荐