scholarly journals Ancient Solutions of Geometric Flows with Curvature Pinching

2018 ◽  
Vol 29 (2) ◽  
pp. 1206-1232 ◽  
Author(s):  
Susanna Risa ◽  
Carlo Sinestrari
Keyword(s):  
Geometric Flows ◽  
Ancient Solutions ◽  
Curvature Pinching

ANCIENT SOLUTIONS OF CODIMENSION TWO SURFACES WITH CURVATURE PINCHING

2020 ◽  
Vol 102 (1) ◽  
pp. 162-171
Author(s):  
ZHENGCHAO JI
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Second Fundamental Form ◽  
Geometric Flows ◽  
Codimension Two ◽  
The Second Fundamental Form ◽  
Ancient Solutions ◽  
The Mean ◽  
Curvature Pinching

We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterise the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces.

scholarly journals Ancient Solutions to Geometric Flows

2020 ◽  
Vol 67 (04) ◽  
pp. 1
Author(s):  
Panagiota Daskalopoulos ◽  
Natasa Sesum
Keyword(s):  
Geometric Flows ◽  
Ancient Solutions

Geometric Flows on Planar Lattices

2021 ◽  
Author(s):  
Andrea Braides ◽  
Margherita Solci
Keyword(s):  
Geometric Flows ◽  
Planar Lattices

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.

Stability of geometric flows of closed forms

2020 ◽  
Vol 364 ◽  
pp. 107030
Author(s):  
Lucio Bedulli ◽  
Luigi Vezzoni
Keyword(s):  
Geometric Flows
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