A group-theoretic method of differential geometric investigation

1964 ◽  
pp. 337-350
Author(s):  
G. F. Laptev
Keyword(s):  
Theoretic Method ◽  
Group Theoretic Method

A group theoretic method for elastic dielectrics

1979 ◽  
Vol 15 (10) ◽  
pp. 795-803 ◽  
Author(s):  
K.L. Chowdhury ◽  
P.G. Glockner
Keyword(s):  
Theoretic Method ◽  
Group Theoretic Method

scholarly journals ON GILP’S GROUP-THEORETIC APPROACH TO FALCONER’S DISTANCE PROBLEM

2020 ◽  
pp. 1-16
Author(s):  
HAN YU
Keyword(s):  
Continuity Condition ◽  
Theoretic Approach ◽  
Borel Sets ◽  
Theoretic Method ◽  
Group Theoretic Method ◽  
Distance Problem ◽  
Distance Sets

Abstract In this paper, we follow and extend a group-theoretic method introduced by Greenleaf–Iosevich–Liu–Palsson (GILP) to study finite points configurations spanned by Borel sets in $\mathbb{R}^n,n\geq 2,n\in\mathbb{N}.$ We remove a technical continuity condition in a GILP’s theorem in [Revista Mat. Iberoamer31 (2015), 799–810]. This allows us to extend the Wolff–Erdogan dimension bound for distance sets to finite points configurations with k points for $k\in\{2,\dots,n+1\}$ forming a $(k-1)$ -simplex.

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