Global continuation in Euclidean spaces of the perturbed unit eigenvectors corresponding to a simple eigenvalue

2020 ◽  
pp. 1
Author(s):  
Pierluigi Benevieri ◽  
Alessandro Calamai ◽  
Massimo Furi ◽  
Maria Patrizia Pera
Keyword(s):  
Simple Eigenvalue ◽  
Euclidean Spaces ◽  
Global Continuation

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 Equiangular lines in Euclidean spaces

2016 ◽  
Vol 138 ◽  
pp. 208-235 ◽  
Author(s):  
Gary Greaves ◽  
Jacobus H. Koolen ◽  
Akihiro Munemasa ◽  
Ferenc Szöllősi
Keyword(s):  
Euclidean Spaces ◽  
Equiangular Lines

scholarly journals Improving the condition number of a simple eigenvalue by a rank one matrix

2016 ◽  
Vol 58 ◽  
pp. 7-12
Author(s):  
Rafael Bru ◽  
Rafael Cantó ◽  
Ana M. Urbano
Keyword(s):  
Condition Number ◽  
Simple Eigenvalue ◽  
Rank One

scholarly journals On embedding of graphs into euclidean spaces of small dimension

1992 ◽  
Vol 56 (1) ◽  
pp. 1-8 ◽  
Author(s):  
J Reiterman ◽  
V Rödl ◽  
E S̆in̆ajová
Keyword(s):  
Small Dimension ◽  
Euclidean Spaces
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