The "hot spots" conjecture on higher dimensional Sierpinski gaskets

2015 ◽  
Vol 15 (1) ◽  
pp. 287-297
Author(s):  
Huo-Jun Ruan ◽  
Xiao-Hui Li
Keyword(s):  
Hot Spots ◽  
Higher Dimensional ◽  
Sierpinski Gaskets ◽  
Hot Spots Conjecture

scholarly journals On the “Hot Spots” Conjecture of J. Rauch

1999 ◽  
Vol 164 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Rodrigo Banuelos ◽  
Krzysztof Burdzy
Keyword(s):  
Hot Spots ◽  
Hot Spots Conjecture

Covering Maps and Periodic Functions on Higher Dimensional Sierpinski Gaskets

2010 ◽  
Vol 61 (5) ◽  
pp. 1151-1181 ◽  
Author(s):  
Huo-Jun Ruan ◽  
Robert S. Strichartz
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Sierpinski Gasket ◽  
Series Expansions ◽  
Periodic Functions ◽  
Sierpiński Gasket ◽  
Higher Dimensional ◽  
Sierpinski Gaskets

Abstract.We construct covering maps from infinite blowups of the$n$-dimensional Sierpinski gasket$S{{G}_{n}}$to certain compact fractafolds based on$S{{G}_{n}}$. These maps are fractal analogs of the usual covering maps fromthe line to the circle. The construction extends work of the second author in the case$n=2$, but a differentmethod of proof is needed, which amounts to solving a Sudoku-type puzzle. We can use the covering maps to define the notion of periodic function on the blowups. We give a characterization of these periodic functions and describe the analog of Fourier series expansions. We study covering maps onto quotient fractalfolds. Finally, we show that such covering maps fail to exist for many other highly symmetric fractals.

A Counterexample to the “Hot Spots” Conjecture on Nested Fractals

2017 ◽  
Vol 24 (1) ◽  
pp. 210-225 ◽  
Author(s):  
Ka-Sing Lau ◽  
Xiao-Hui Li ◽  
Huo-Jun Ruan
Keyword(s):  
Hot Spots ◽  
Hot Spots Conjecture

scholarly journals A Counterexample to the "Hot Spots" Conjecture

1999 ◽  
Vol 149 (1) ◽  
pp. 309 ◽  
Author(s):  
Krzysztof Burdzy ◽  
Wendelin Werner
Keyword(s):  
Hot Spots ◽  
Hot Spots Conjecture

Hot spots conjecture for a class of acute triangles

2015 ◽  
Vol 280 (3-4) ◽  
pp. 783-806 ◽  
Author(s):  
Bartłomiej Siudeja
Keyword(s):  
Hot Spots ◽  
Hot Spots Conjecture

An inequality for potentials and the 'hot-spots' conjecture

2004 ◽  
Vol 53 (1) ◽  
pp. 35-48 ◽  
Author(s):  
Rodrigo Banuelos ◽  
Michael Pang
Keyword(s):  
Hot Spots ◽  
Hot Spots Conjecture
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