scholarly journals The domino problem on groups of polynomial growth

2018 ◽  
Vol 12 (1) ◽  
pp. 93-105
Author(s):  
Alexis Ballier ◽  
Maya Stein
2012 ◽  
Vol 212 (2) ◽  
pp. 119-139 ◽  
Author(s):  
Isabelle Gallagher ◽  
Yannick Sire

2003 ◽  
Vol 245 (4) ◽  
pp. 791-821 ◽  
Author(s):  
G. Fendler ◽  
K. Gr�chenig ◽  
M. Leinert ◽  
J. Ludwig ◽  
C. Molitor-Braun

1999 ◽  
Vol 162 (1) ◽  
pp. 14-51 ◽  
Author(s):  
A.F.M. ter Elst ◽  
Derek W. Robinson ◽  
Adam Sikora

Author(s):  
Hélène Perrin

AbstractWe study upper bounds for the first non-zero eigenvalue of the Steklov problem defined on finite graphs with boundary. For finite graphs with boundary included in a Cayley graph associated to a group of polynomial growth, we give an upper bound for the first non-zero Steklov eigenvalue depending on the number of vertices of the graph and of its boundary. As a corollary, if the graph with boundary also satisfies a discrete isoperimetric inequality, we show that the first non-zero Steklov eigenvalue tends to zero as the number of vertices of the graph tends to infinity. This extends recent results of Han and Hua, who obtained a similar result in the case of $$\mathbb {Z}^n$$ Z n . We obtain the result using metric properties of Cayley graphs associated to groups of polynomial growth.


Sign in / Sign up

Export Citation Format

Share Document