A Note on Finsler Version of Calabi-Yau Theorem

被引：7
作者：
Yin, Songting [1 ,2 ]
Wang, Ruixin [3 ]
Zhang, Pan [3 ,4 ]
机构：
[1] Tongling Univ, Dept Math & Comp Sci, Tongling 244000, Anhui, Peoples R China
[2] Fujian Prov Univ, Putian Univ, Key Lab Appl Math, Putian 351100, Fujian, Peoples R China
[3] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
[4] Sun Yat Sen Univ, Sch Math, Guangzhou, Guangdong, Peoples R China
来源：
ADVANCES IN MATHEMATICAL PHYSICS | 2018年 / 2018卷
关键词：
COMPLETE RIEMANNIAN-MANIFOLDS; GEOMETRY;
D O I：
10.1155/2018/1761608
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We generalize Calabi-Yau's linear volume growth theorem to Finsler manifold with the weighted Ricci curvature bounded below by a negative function and show that such a manifold must have infinite volume.
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收藏
页数：4
相关论文
共 12 条
[1]  
Calabi E., 1975, NOTICES AM MATH SOC, V22, pA
[2]  
CHEEGER J, 1982, J DIFFER GEOM, V17, P15
[3]   Some properties of non-compact complete Riemannian manifolds [J].
Ma, Li .
BULLETIN DES SCIENCES MATHEMATIQUES, 2006, 130 (04) :330-336
[4]   Finsler interpolation inequalities [J].
Ohta, Shin-ichi .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2009, 36 (02) :211-249
[5]   Heat Flow on Finsler Manifolds [J].
Ohta, Shin-Ichi ;
Sturm, Karl-Theodor .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (10) :1386-1433
[6]   A sphere theorem for non-reversible Finsler metrics [J].
Rademacher, HB .
MATHEMATISCHE ANNALEN, 2004, 328 (03) :373-387
[7]   Volume comparison and its applications in Riemann-Finsler geometry [J].
Shen, ZM .
ADVANCES IN MATHEMATICS, 1997, 128 (02) :306-328
[8]   Comparison theorems in Finsler geometry and their applications [J].
Wu, B. Y. ;
Xin, Y. L. .
MATHEMATISCHE ANNALEN, 2007, 337 (01) :177-196
[9]   Volume form and its applications in Finsler geometry [J].
Wu, Bing Ye .
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2011, 78 (3-4) :723-741
[10]   SOME FUNCTION-THEORETIC PROPERTIES OF COMPLETE RIEMANNIAN MANIFOLD AND THEIR APPLICATIONS TO GEOMETRY [J].
YAU, ST .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1976, 25 (07) :659-670
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