SOBOLEV-TYPE INEQUALITIES AND COMPLETE RIEMANNIAN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE

被引：0

作者：

Abolarinwa, Abimbola ^{[1
]}

Adefolarin, Adekunle ^{[2
]}

Animasahun, Isaac A. ^{[3
]}

机构：

[1] Landmark Univ, Dept Phys Sci, PMB 1001, Omu Aran, Kwara State, Nigeria

[2] Fed Polytech, Dept Stat, Ado Ekiti, Ekiti State, Nigeria

[3] Osun State Coll Educ, Dept Math, Ila Orangun, Osun State, Nigeria

来源：

BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 11卷 / 01期

关键词：

Sobolev inequalities; best constant; Ricci tensor; heat kernel; UPPER-BOUNDS; HEAT; KERNELS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be an n-dimensional complete Riemannian manifold, we investigate the geometric nature of such M which admits any of the family of Sobolev-type inequalities with the optimal Euclidean Sobolev constant. This leads to several conditions under which M with nonnegative Ricci curvature is isometric to Euclidean space R-n.

引用

页码：11 / 21

页数：11

共 50 条

[41] Sharp Morrey-Sobolev Inequalities on Complete Riemannian Manifolds
Alexandru Kristály
[J]. Potential Analysis, 2015, 42 : 141 - 154
[42] Noncompact manifolds with nonnegative Ricci curvature
William C. Wylie
[J]. The Journal of Geometric Analysis, 2006, 16 : 535 - 550
[43] MANIFOLDS OF ALMOST NONNEGATIVE RICCI CURVATURE
YAMAGUCHI, T
[J]. JOURNAL OF DIFFERENTIAL GEOMETRY, 1988, 28 (01) : 157 - 167
[44] Noncompact manifolds with nonnegative Ricci curvature
Wylie, William C.
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2006, 16 (03) : 535 - 550
[45] Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature
Cheeger, J
Colding, TH
Minicozzi, WP
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 1995, 5 (06) : 948 - 954
[46] Complete manifolds with nonnegative Ricci curvature and quadratically nonnegatively curved infinity
Sha, JP
Shen, ZM
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1997, 119 (06) : 1399 - 1404
[47] Diameter growth and bounded topology of complete manifolds with nonnegative Ricci curvature
Huihong Jiang
Yi-Hu Yang
[J]. Annals of Global Analysis and Geometry, 2017, 51 : 359 - 366
[48] Complete manifolds with asymptotically nonnegative Ricci curvature and weak bounded geometry
Zisheng Hu
Senlin Xu
[J]. Archiv der Mathematik, 2007, 88 : 455 - 467
[49] THE CLASSIFICATION OF COMPLETE LOCALLY CONFORMALLY FLAT MANIFOLDS OF NONNEGATIVE RICCI CURVATURE
ZHU, SH
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1994, 163 (01) : 189 - 199
[50] Complete manifolds with asymptotically nonnegative Ricci curvature and weak bounded geometry
Hu, Zisheng
Xu, Senlin
[J]. ARCHIV DER MATHEMATIK, 2007, 88 (05) : 455 - 467

← 1 2 3 4 5 →