scholarly journals Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group

2017 ◽  
Vol 22 (8) ◽  
pp. 909-936 ◽  
Author(s):  
Andrei A. Ardentov ◽  
Yuri L. Sachkov
Keyword(s):  
Cut Locus ◽  
Engel Group ◽  
Maxwell Strata

Cut Locus in the Sub-Riemannian Problem on Engel Group

2018 ◽  
Vol 97 (1) ◽  
pp. 82-85 ◽  
Author(s):  
A. A. Ardentov ◽  
Yu. L. Sachkov
Keyword(s):  
Cut Locus ◽  
Engel Group

On 4-Engel Groups

2007 ◽  
Vol 10 ◽  
pp. 341-353 ◽  
Author(s):  
Michael Vaughan-Lee
Keyword(s):  
Normal Closure ◽  
Engel Group

In this note, the author proves that a group G is a 4-Engel group if and only if the normal closure of every element g ∈ G is a 3-Engel group

Practical Computation of the Cut Locus on Discrete Surfaces

2021 ◽  
Vol 40 (5) ◽  
pp. 261-273
Author(s):  
C. Mancinelli ◽  
M. Livesu ◽  
E. Puppo
Keyword(s):  
Cut Locus ◽  
Practical Computation ◽  
Discrete Surfaces

scholarly journals Remarks on Manifolds with Two-Sided Curvature Bounds

2021 ◽  
Vol 9 (1) ◽  
pp. 53-64
Author(s):  
Vitali Kapovitch ◽  
Alexander Lytchak
Keyword(s):  
Distance Functions ◽  
Cut Locus ◽  
Bounded Curvature ◽  
Curvature Bounds ◽  
Positive Reach

Abstract We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

Extremal trajectories in a nilpotent sub-Riemannian problem on the Engel group

2011 ◽  
Vol 202 (11) ◽  
pp. 1593-1615 ◽  
Author(s):  
Andrei A Ardentov ◽  
Yurii L Sachkov
Keyword(s):  
Engel Group ◽  
Extremal Trajectories

The Lorentzian Cut Locus

2017 ◽  
pp. 295-322
Author(s):  
John K. Beem ◽  
Paul E. Ehrlich ◽  
Kevin L. Easley
Keyword(s):  
Cut Locus
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