Resistance Forms, Quasisymmetric Maps and Heat Kernel Estimates

(Memoirs of the American Mathematical Society)

5c6d2580005eb.jpg Author Jun Kigami
Isbn 9780821852996
File size 1.02MB
Year 2012
Pages 132
Language English
File format PDF
Category Mathematics

Book Description:

Assume that there is some analytic structure, a differential equation or a stochastic process for example, on a metric space. To describe asymptotic behaviors of analytic objects, the original metric of the space may not be the best one. Every now and then one can construct a better metric which is somehow "intrinsic" with respect to the analytic structure and under which asymptotic behaviors of the analytic objects have nice expressions. The problem is when and how one can find such a metric. In this paper, the author considers the above problem in the case of stochastic processes associated with Dirichlet forms derived from resistance forms. The author's main concerns are the following two problems: (I) When and how to find a metric which is suitable for describing asymptotic behaviors of the heat kernels associated with such processes. (II) What kind of requirement for jumps of a process is necessary to ensure good asymptotic behaviors of the heat kernels associated with such processes.

 

 

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