A new local gradient estimate for a nonlinear equation under integral curvature condition on manifolds

2020 ◽  
Vol 306 (2) ◽  
pp. 755-765
Author(s):  
Liang Zhao ◽  
Shouwen Fang
Keyword(s):  
Nonlinear Equation ◽  
Gradient Estimate ◽  
Integral Curvature ◽  
Curvature Condition ◽  
Local Gradient

A note on a three-dimensional sphere theorem with integral curvature condition

2016 ◽  
Vol 18 (04) ◽  
pp. 1550070 ◽  
Author(s):  
Mijia Lai
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Space Form ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Integral Curvature ◽  
Spherical Space ◽  
Sphere Theorem ◽  
Curvature Condition ◽  
Spherical Space Form

In this paper, we obtain a three-dimensional sphere theorem with integral curvature condition. On a closed three manifold [Formula: see text] with constant positive scalar curvature, if a certain combination of [Formula: see text] norm of the Ricci curvature and [Formula: see text] norm of the scalar curvature is positive, then [Formula: see text] is diffeomorphic to a spherical space form.

scholarly journals Zhong–Yang type eigenvalue estimate with integral curvature condition

2019 ◽  
Vol 296 (1-2) ◽  
pp. 595-613
Author(s):  
Xavier Ramos Olivé ◽  
Shoo Seto ◽  
Guofang Wei ◽  
Qi S. Zhang
Keyword(s):  
Integral Curvature ◽  
Eigenvalue Estimate ◽  
Curvature Condition
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