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Isoperimetric constants and estimates of heat kernels of pre Sierpinski carpets
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  • Published: December 1990

Isoperimetric constants and estimates of heat kernels of pre Sierpinski carpets

  • Hirofumi Osada1 

Probability Theory and Related Fields volume 86, pages 469–490 (1990)Cite this article

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  • 17 Citations

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Summary

The author calculated isoperimetric constants of then-dimensional pre Sierpinski carpetY n . As an application, he obtained the following estimate of the Neumann heat kernelp n (t, x, y) onY n ;

where

$$d\left( n \right) = \log \left( {3^n - 1} \right)/\left\{ {\log \left( {3^n - 1} \right) - \log \left( {3^{n - 1} - 1} \right)} \right\}$$

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References

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Tokyo, Hongo, 113, Tokyo, Japan

    Hirofumi Osada

Authors
  1. Hirofumi Osada
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Cite this article

Osada, H. Isoperimetric constants and estimates of heat kernels of pre Sierpinski carpets. Probab. Th. Rel. Fields 86, 469–490 (1990). https://doi.org/10.1007/BF01198170

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  • Received: 09 December 1988

  • Revised: 19 March 1990

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01198170

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Heat Kernel
  • Sierpinski Carpet
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