scholarly journals Hausdorff convergence and universal covers

2001 ◽  
Vol 353 (9) ◽  
pp. 3585-3602 ◽  
Author(s):  
Christina Sormani ◽  
Guofang Wei
Keyword(s):  
Hausdorff Convergence ◽  
Universal Covers

scholarly journals Smallest universal covers for families of triangles

2021 ◽  
Vol 92 ◽  
pp. 101686
Author(s):  
Ji-won Park ◽  
Otfried Cheong
Keyword(s):  
Universal Covers

scholarly journals Revisiting Leighton’s theorem with the Haar measure

2020 ◽  
pp. 1-9
Author(s):  
DANIEL J. WOODHOUSE
Keyword(s):  
Haar Measure ◽  
Free Groups ◽  
Finite Cover ◽  
Covering Theorem ◽  
Rigidity Result ◽  
Graph Covering ◽  
Finite Graphs ◽  
Universal Covers ◽  
Line Patterns

Abstract Leighton’s graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton’s theorem that allows generalisations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen–Macura and Hagen–Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups.

Galois action on universal covers of Kodaira fibrations

2020 ◽  
Vol 169 (7) ◽  
pp. 1281-1303
Author(s):  
Gabino González-Diez
Keyword(s):  
Galois Action ◽  
Universal Covers

A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION

2011 ◽  
Vol 21 (10) ◽  
pp. 2019-2047 ◽  
Author(s):  
GIULIANO LAZZARONI ◽  
RODICA TOADER
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
A Priori ◽  
Brittle Materials ◽  
Continuity Property ◽  
Vanishing Viscosity ◽  
Hausdorff Convergence ◽  
Linearized Elasticity

In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.

Sign in / Sign up

Export Citation Format

Share Document