scholarly journals Higher-order estimates of long-time solutions to the Kähler-Ricci flow

2021 ◽  
Vol 281 (11) ◽  
pp. 109235
Author(s):  
Frederick Tsz-Ho Fong ◽  
Man-Chun Lee
Keyword(s):  
Ricci Flow ◽  
Higher Order ◽  
Long Time

scholarly journals PHASE PORTRAIT OF SECOND-ORDER DYNAMIC SYSTEMS

2018 ◽  
Vol 6 (3) ◽  
pp. 252-262 ◽  
Author(s):  
Kaloyan Yankov
Keyword(s):  
Phase Portrait ◽  
Plasma Renin ◽  
Higher Order ◽  
Second Order ◽  
Graphical Form ◽  
Time Behavior ◽  
Long Time ◽  
Phase Plane Method ◽  
The Stability ◽  
Higher Order Differential Equations

The phase portrait of the second and higher order differential equations presents in graphical form the behavior of the solution set without solving the equation. In this way, the stability of a dynamic system and its long-time behavior can be studied. The article explores the capabilities of Mathcad for analysis of systems by the phase plane method. A sequence of actions using Mathcad's operators to build phase portrait and phase trace analysis is proposed. The approach is illustrated by a model of plasma renin activity after treatment of experimental animals with nicardipine. The identified process is a differential equation of the second order. The algorithm is also applicable to systems of higher order.

scholarly journals The Long-Time Behavior of the Ricci Tensor under the Ricci Flow

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Christian Hilaire
Keyword(s):  
Ricci Flow ◽  
Ricci Tensor ◽  
Closed Manifold ◽  
Time Behavior ◽  
Dimensional Manifold ◽  
Long Time Behavior ◽  
Bounded Curvature ◽  
3 Dimensional ◽  
Long Time ◽  
Uniformly Bounded

We show that, given an immortal solution to the Ricci flow on a closed manifold with uniformly bounded curvature and diameter, the Ricci tensor goes to zero as . We also show that if there exists an immortal solution on a closed 3-dimensional manifold such that the product of the curvature and the square of the diameter is uniformly bounded, then this solution must be of type III.

THE SASAKI–RICCI FLOW

2010 ◽  
Vol 21 (07) ◽  
pp. 951-969 ◽  
Author(s):  
KNUT SMOCZYK ◽  
GUOFANG WANG ◽  
YONGBING ZHANG
Keyword(s):  
Ricci Flow ◽  
Einstein Metrics ◽  
Positive Case ◽  
Einstein Metric ◽  
Well Posedness ◽  
Long Time Existence ◽  
Null Case ◽  
Long Time ◽  
Time Existence

In this paper, we introduce the Sasaki–Ricci flow to study the existence of η-Einstein metrics. In the positive case any η-Einstein metric can be homothetically transformed to a Sasaki–Einstein metric. Hence it is an odd-dimensional counterpart of the Kähler–Ricci flow. We prove its well-posedness and long-time existence. In the negative or null case the flow converges to the unique η-Einstein metric. In the positive case the convergence remains in general open. The paper can be viewed as an odd-dimensional counterpart of Cao's results on the Kähler–Ricci flow.

scholarly journals Long time behaviour of Ricci flow on open 3-manifolds

2015 ◽  
Vol 90 (2) ◽  
pp. 377-405
Author(s):  
Laurent Bessières ◽  
Gérard Besson ◽  
Sylvain Maillot
Keyword(s):  
Ricci Flow ◽  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time
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