HEAT KERNEL ESTIMATES ON JULIA SETS

Meng YANG

doi:10.1016/S0252-9602(17)30081-4

Acta mathematica scientia, Series B >

2017 , Vol. 37 >Issue 5: 1399 - 1414

DOI: https://doi.org/10.1016/S0252-9602(17)30081-4

Articles

HEAT KERNEL ESTIMATES ON JULIA SETS

Meng YANG

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Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received date: 2016-01-08

Revised date: 2017-04-27

Online published: 2017-10-25

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Abstract

We give heat kernel estimates on Julia sets J (f_c) for quadratic polynomials f_c (z)=z²+c for c in the main cardioid or the ±(1)/k-bulbs where k ≥ 2.First we use external ray parametrization to construct a regular,strongly local and conservative Dirichlet form on Julia set.Then we show that this Dirichlet form is a resistance form and the corresponding resistance metric induces the same topology as Euclidean metric.Finally,we give heat kernel estimates under the resistance metric.

Key words： Julia sets; heat kernel; resistance metric

Cite this article

Meng YANG . HEAT KERNEL ESTIMATES ON JULIA SETS[J]. Acta mathematica scientia, Series B, 2017 , 37(5) : 1399 -1414 . DOI: 10.1016/S0252-9602(17)30081-4

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