scholarly journals The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature

2017 ◽  
Vol 145 (5) ◽  
pp. 2199-2210 ◽  
Author(s):  
Christian Rose ◽  
Peter Stollmann
Keyword(s):  
Ricci Curvature ◽  
Compact Manifolds ◽  
Negative Part ◽  
Kato Class

scholarly journals Gaussian heat kernel estimates: From functions to forms

2020 ◽  
Vol 2020 (761) ◽  
pp. 25-79
Author(s):  
Thierry Coulhon ◽  
Baptiste Devyver ◽  
Adam Sikora
Keyword(s):  
Riemannian Manifold ◽  
Heat Kernel ◽  
Ricci Curvature ◽  
Compact Riemannian Manifold ◽  
Kernel Estimates ◽  
Doubling Property ◽  
Negative Part ◽  
Heat Kernel Estimates ◽  
Volume Doubling ◽  
Upper Estimate

AbstractOn a complete non-compact Riemannian manifold satisfying the volume doubling property, we give conditions on the negative part of the Ricci curvature that ensure that, unless there are harmonic 1-forms, the Gaussian heat kernel upper estimate on functions transfers to one-forms. These conditions do no entail any constraint on the size of the Ricci curvature, only on its decay at infinity.

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