QUASISYMMETRIC UNIFORMIZATION AND HEAT KERNEL ESTIMATES

被引：7
|
作者：
Murugan, Mathav [1 ]
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 06期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Quasisymmetry; uniformization; circle packing; sub-Gaussian estimate; Harnack inequality; PLANAR GRAPHS; HARNACK INEQUALITIES; HARMONIC-FUNCTIONS; VOLUME GROWTH; RANDOM-WALKS; STABILITY; BOUNDARY; CAPACITY; SPACES;
D O I：
10.1090/tran/7713
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the circle packing embedding in R-2 of a one-ended, planar triangulation with polynomial growth is quasisymmetric if and only if the simple random walk on the graph satisfies sub-Gaussian heat kernel estimate with spectral dimension two. Our main results provide a new family of graphs and fractals that satisfy sub-Gaussian estimates and Harnack inequalities.
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页码：4177 / 4209
页数：33
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