scholarly journals Rate of curvature decay for the contracting cusp Ricci flow

2020 ◽  
Vol 28 (5) ◽  
pp. 1221-1250
Author(s):  
Peter M. Topping ◽  
Hao Yin
Keyword(s):  
Ricci Flow ◽  
Curvature Decay

The Kähler-Ricci mean curvature flow of a strictly area decreasing map Between Riemann Surfaces

2020 ◽  
Vol 31 (08) ◽  
pp. 2050061
Author(s):  
Shujing Pan
Keyword(s):  
Scalar Curvature ◽  
Ricci Flow ◽  
Mean Curvature ◽  
Riemann Surfaces ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Positive Scalar Curvature ◽  
Curvature Decay ◽  
The Mean ◽  
Compact Riemann Surfaces

Suppose that [Formula: see text] is a product of compact Riemann surfaces [Formula: see text],[Formula: see text], i.e. [Formula: see text], and [Formula: see text] is a graph in [Formula: see text] of a strictly area dereasing map [Formula: see text]. Let [Formula: see text] evolve along the Kähler–Ricci flow, and [Formula: see text] in [Formula: see text] evolve along the mean curvature flow. We show that [Formula: see text] remains to be a graph of a strictly area decreasing map along the Kähler–Ricci mean curvature flow and exists for all time. In the positive scalar curvature case, we prove the convergence of the flow and the curvature decay along the flow at infinity.

Ricci Flow on Quasi Einstein Manifold

2010 ◽  
Vol 0 (-1) ◽  
pp. 447-454
Author(s):  
A. Bhattacharyya ◽  
T. De
Keyword(s):  
Ricci Flow ◽  
Einstein Manifold

scholarly journals Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

scholarly journals Sliding Mode Control and Geometrization Conjecture in Seismic Response

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 353
Author(s):  
Ligia Munteanu ◽  
Dan Dumitriu ◽  
Cornel Brisan ◽  
Mircea Bara ◽  
Veturia Chiroiu ◽  
...  
Keyword(s):  
Sliding Mode Control ◽  
Ricci Flow ◽  
Lyapunov Functions ◽  
Seismic Waves ◽  
Sliding Mode ◽  
Flow Process ◽  
Mode Control ◽  
Finite Period ◽  
The Stability ◽  
Story Building

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

scholarly journals Ancient solutions for Andrews’ hypersurface flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Peng Lu ◽  
Jiuru Zhou
Keyword(s):  
Ricci Flow ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Euclidean Spaces ◽  
Round Cylinder ◽  
Ancient Solutions ◽  
Singular Time

AbstractWe construct the ancient solutions of the hypersurface flows in Euclidean spaces studied by B. Andrews in 1994.As time {t\rightarrow 0^{-}} the solutions collapse to a round point where 0 is the singular time. But as {t\rightarrow-\infty} the solutions become more and more oval. Near the center the appropriately-rescaled pointed Cheeger–Gromov limits are round cylinder solutions {S^{J}\times\mathbb{R}^{n-J}}, {1\leq J\leq n-1}. These results are the analog of the corresponding results in Ricci flow ({J=n-1}) and mean curvature flow.

scholarly journals Ricci flow on surfaces with cusps

2009 ◽  
Vol 345 (4) ◽  
pp. 819-834 ◽  
Author(s):  
Lizhen Ji ◽  
Rafe Mazzeo ◽  
Natasa Sesum
Keyword(s):  
Ricci Flow
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