$L^p$ Harmonic $k$-forms on Complete Noncompact Hypersurfaces in $\mathbb{S}^{n+1}$ with Finite Total Curvature

2021 ◽  
Vol 54 (4) ◽  
pp. 396-406
Author(s):  
global JiuruZhou
Keyword(s):  
Total Curvature ◽  
Finite Total Curvature

Harmonic p-forms on Hadamard manifolds with finite total curvature

2018 ◽  
Vol 54 (4) ◽  
pp. 473-487
Author(s):  
Peijun Wang ◽  
Xiaoli Chao ◽  
Yilong Wu ◽  
Yusha lv
Keyword(s):  
Total Curvature ◽  
Hadamard Manifolds ◽  
Finite Total Curvature

scholarly journals The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces

2013 ◽  
Vol 209 ◽  
pp. 23-34 ◽  
Author(s):  
Minoru Tanaka ◽  
Kei Kondo
Keyword(s):  
Total Curvature ◽  
Comparison Theorems ◽  
Surfaces Of Revolution ◽  
Model Surface ◽  
Open Manifold ◽  
Finite Total Curvature ◽  
Radial Curvature ◽  
Noncompact Riemannian Manifold ◽  
Sectional Curvatures ◽  
Noncompact Riemannian Manifolds

AbstractWe construct distinctive surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comparison theorems in radial curvature geometry. Moreover, we prove that a complete noncompact Riemannian manifold M is homeomorphic to the interior of a compact manifold with boundary if the manifold M is not less curved than a noncompact model surface of revolution and if the total curvature of the model surface is finite and less than 2π. By the first result mentioned above, the second result covers a much wider class of manifolds than that of complete noncompact Riemannian manifolds whose sectional curvatures are bounded from below by a constant.

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