Rectifiable curves in Sierpinski carpets

2011 ◽  
Vol 60 (1) ◽  
pp. 285-310 ◽  
Author(s):  
Estibalitz Durand-Cartagena ◽  
Jeremy T. Tyson
Keyword(s):  
Rectifiable Curves ◽  
Sierpinski Carpets

Critical exponents for Ising-like systems on Sierpinski carpets

1987 ◽  
Vol 48 (4) ◽  
pp. 553-558 ◽  
Author(s):  
B. Bonnier ◽  
Y. Leroyer ◽  
C. Meyers
Keyword(s):  
Critical Exponents ◽  
Sierpinski Carpets

scholarly journals Brownian Motion and Harmonic Analysis on Sierpinski Carpets

1999 ◽  
Vol 51 (4) ◽  
pp. 673-744 ◽  
Author(s):  
Martin T. Barlow ◽  
Richard F. Bass
Keyword(s):  
Brownian Motion ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Heat Kernel ◽  
Lower Bounds ◽  
Harnack Inequality ◽  
Harmonic Functions ◽  
Upper And Lower Bounds ◽  
Isotropic Diffusion ◽  
Sierpinski Carpets

AbstractWe consider a class of fractal subsets of d formed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusion X and determine its basic properties; and extend some classical Sobolev and Poincaré inequalities to this setting.

scholarly journals Conformal welding of rectifiable curves.

1990 ◽  
Vol 67 ◽  
pp. 61 ◽  
Author(s):  
Christopher J. Bishop
Keyword(s):  
Conformal Welding ◽  
Rectifiable Curves

The Critical Behavior of Partially Directed SAW on Sierpinski Carpets

1991 ◽  
Vol 16 (3) ◽  
pp. 355-358 ◽  
Author(s):  
Kai-Lun Yao ◽  
Guo-Ce Zhuang ◽  
Jia-Fu Wang
Keyword(s):  
Critical Behavior ◽  
Sierpinski Carpets
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