scholarly journals Asymptotics of Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space

2020 ◽  
Vol 16 (1) ◽  
pp. 195-208
Author(s):  
A.P. Mashtakov ◽  
◽  
A.Y. Popov ◽  
Keyword(s):  
Euclidean Space ◽  
Group Of Motions

scholarly journals Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space

2017 ◽  
Vol 22 (8) ◽  
pp. 949-954 ◽  
Author(s):  
Alexey P. Mashtakov ◽  
Anton Yu. Popov
Keyword(s):  
Euclidean Space ◽  
Group Of Motions

Domain of attraction of a stable law for the group of motions of Euclidean space

1985 ◽  
Vol 25 (3) ◽  
pp. 219-228
Author(s):  
A. Grincevičius
Keyword(s):  
Euclidean Space ◽  
Domain Of Attraction ◽  
Stable Law ◽  
Group Of Motions

Domain of attraction of a stable law for the group of motions of Euclidean space

1990 ◽  
Vol 30 (1) ◽  
pp. 8-19
Author(s):  
A. Grincevičius
Keyword(s):  
Euclidean Space ◽  
Domain Of Attraction ◽  
Stable Law ◽  
Group Of Motions

Compactification of Submanifolds in Euclidean Space by the Inversion

2018 ◽  
Author(s):  
Kazuyuki Enomoto
Keyword(s):  
Euclidean Space

Symplectic capacities

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Euclidean Space ◽  
Generating Functions ◽  
Weinstein Conjecture ◽  
Finite Dimensional ◽  
Hofer Metric

This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existence gives rise to a proof of the Weinstein conjecture for hypersurfaces of Euclidean space. The last section contains a proof that the Hofer–Zehnder capacity satisfies the required axioms. This proof translates the Hofer–Zehnder variational argument into the setting of (finite-dimensional) generating functions.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

On the Rigidity Theorems for Entire Lagrangian Translating Solitons in Pseudo-Euclidean Space IV

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Yadong Wu ◽  
Ruiwei Xu
Keyword(s):  
Euclidean Space ◽  
Rigidity Theorems ◽  
Translating Solitons
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