Vanishing theorems for p-harmonic ℓ-forms on Riemannian manifolds with a weighted Poincaré inequality

2021 ◽  
Vol 76 ◽  
pp. 101741
Author(s):  
Xiaoli Chao ◽  
Aiying Hui ◽  
Miaomiao Bai
Keyword(s):  
Riemannian Manifolds ◽  
Poincaré Inequality ◽  
Vanishing Theorems ◽  
Poincare Inequality ◽  
Weighted Poincaré Inequality

scholarly journals L 2 harmonic forms and finiteness of ends

2013 ◽  
Vol 85 (2) ◽  
pp. 457-471 ◽  
Author(s):  
PENG ZHU
Keyword(s):  
Riemannian Manifolds ◽  
Poincaré Inequality ◽  
Vanishing Theorems ◽  
Poincare Inequality ◽  
Harmonic Forms ◽  
Minimal Hypersurfaces ◽  
Weighted Poincaré Inequality ◽  
Complete Riemannian Manifolds

In this paper, we obtain vanishing theorems and finitely many ends theorems of complete Riemannian manifolds with weighted Poincaré inequality, applying them to minimal hypersurfaces.

scholarly journals Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications

2012 ◽  
Vol 206 ◽  
pp. 25-37
Author(s):  
Hai-Ping Fu ◽  
Deng-Yun Yang
Keyword(s):  
Harmonic Map ◽  
Poincaré Inequality ◽  
Vanishing Theorems ◽  
Poincare Inequality ◽  
Noncompact Manifolds ◽  
Weighted Poincaré Inequality ◽  
Complete Manifolds

AbstractTwo vanishing theorems for harmonic map andL2harmonic 1-form on complete noncompact manifolds are proved under certain geometric assumptions, which generalize results of [13], [15], [18], [19], and [20]. As applications, we improve some main results in [2], [4], [6], [9], [12], [20], [22], [24], and [25].

scholarly journals Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications

2012 ◽  
Vol 206 ◽  
pp. 25-37 ◽  
Author(s):  
Hai-Ping Fu ◽  
Deng-Yun Yang
Keyword(s):  
Harmonic Map ◽  
Poincaré Inequality ◽  
Vanishing Theorems ◽  
Poincare Inequality ◽  
Noncompact Manifolds ◽  
Weighted Poincaré Inequality ◽  
Complete Manifolds

AbstractTwo vanishing theorems for harmonic map and L2 harmonic 1-form on complete noncompact manifolds are proved under certain geometric assumptions, which generalize results of [13], [15], [18], [19], and [20]. As applications, we improve some main results in [2], [4], [6], [9], [12], [20], [22], [24], and [25].

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