scholarly journals Sharp gradient estimates for a heat equation in Riemannian manifolds

2019 ◽  
Vol 147 (12) ◽  
pp. 5329-5338 ◽  
Author(s):  
Ha Tuan Dung ◽  
Nguyen Thac Dung
Keyword(s):  
Heat Equation ◽  
Riemannian Manifolds ◽  
Gradient Estimates

Some New Results on L2 Cohomology of Negatively Curved Riemannian Manifolds

2005 ◽  
Vol 57 (2) ◽  
pp. 251-266
Author(s):  
M. Cocos
Keyword(s):  
Heat Equation ◽  
Riemannian Manifolds ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Regularity Properties ◽  
L2 Cohomology ◽  
Cohomology Spaces

AbstractThe present paper is concerned with the study of the L2 cohomology spaces of negatively curved manifolds. The first half presents a finiteness and vanishing result obtained under some curvature assumptions, while the second half identifies a class of metrics having non-trivial L2 cohomology for degree equal to the half dimension of the space. For the second part we rely on the existence and regularity properties of the solution for the heat equation for forms.

GRADIENT ESTIMATES VIA TWO-POINT FUNCTIONS FOR PARABOLIC EQUATIONS UNDER RICCI FLOW

2020 ◽  
Vol 102 (2) ◽  
pp. 319-330
Author(s):  
MIN CHEN
Keyword(s):  
Riemannian Manifolds ◽  
Ricci Flow ◽  
Parabolic Equations ◽  
Gradient Estimates ◽  
Quasilinear Parabolic Equations ◽  
Quasilinear Parabolic

We derive estimates relating the values of a solution at any two points to the distance between the points for quasilinear parabolic equations on compact Riemannian manifolds under Ricci flow.

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