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.
引用
收藏
页码：4177 / 4209
页数：33
相关论文
共 50 条
  • [21] Exponential divergence estimates and heat kernel tail
    Nualart, E
    COMPTES RENDUS MATHEMATIQUE, 2004, 338 (01) : 77 - 80
  • [22] Heat Kernel Estimates Using Effective Resistance
    Kumagai, Takashi
    RANDOM WALKS ON DISORDERED MEDIA AND THEIR SCALING LIMITS: ECOLE D'ETE DE PROBABILITES DE SAINT-FLOUR XL - 2010, 2014, 2101 : 43 - 58
  • [23] Heat kernel estimates for the Dirichlet fractional Laplacian
    Chen, Zhen-Qing
    Kim, Panki
    Song, Renming
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2010, 12 (05) : 1307 - 1329
  • [24] Symmetric jump processes and their heat kernel estimates
    Chen Zhen-Qing
    SCIENCE IN CHINA SERIES A-MATHEMATICS, 2009, 52 (07): : 1423 - 1445
  • [25] Estimates on the heat kernel of parabolic equations with advection
    Hill, AT
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1997, 28 (06) : 1309 - 1316
  • [26] Heat kernel estimates for operators with boundary conditions
    Daners, D
    MATHEMATISCHE NACHRICHTEN, 2000, 217 : 13 - 41
  • [27] On the dichotomy in the heat kernel two sided estimates
    Grigor'yan, Alexander
    Kumagai, Takashi
    ANALYSIS ON GRAPHS AND ITS APPLICATIONS, 2008, 77 : 199 - +
  • [28] DIRICHLET HEAT KERNEL ESTIMATES FOR Δα/2 + Δβ/2
    Chen, Zhen-Qing
    Kim, Panki
    Song, Renming
    ILLINOIS JOURNAL OF MATHEMATICS, 2010, 54 (04) : 1357 - 1392
  • [29] Lifespan estimates via Neumann heat kernel
    Xin Yang
    Zhengfang Zhou
    Zeitschrift für angewandte Mathematik und Physik, 2019, 70
  • [30] Heat Kernel Estimates for Random Weighted Graphs
    Kumagai, Takashi
    RANDOM WALKS ON DISORDERED MEDIA AND THEIR SCALING LIMITS: ECOLE D'ETE DE PROBABILITES DE SAINT-FLOUR XL - 2010, 2014, 2101 : 59 - 64
12345