Abstract
For the measurable Riemannian structure on the Sierpinski gasket introduced by Kigami, various short time asymptotics of the associated heat kernel are established, including Varadhan’s asymptotic relation, some sharp one-dimensional asymptotics at vertices, and a non-integer-dimensional on-diagonal behavior at almost every point. Moreover, it is also proved that the asymptotic order of the eigenvalues of the corresponding Laplacian is given by the Hausdorff and box-counting dimensions of the space.
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JSPS Research Fellow PD (20·6088): The author is supported by the Japan Society for the Promotion of Science.
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Kajino, N. Heat Kernel Asymptotics for the Measurable Riemannian Structure on the Sierpinski Gasket. Potential Anal 36, 67–115 (2012). https://doi.org/10.1007/s11118-011-9221-5
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DOI: https://doi.org/10.1007/s11118-011-9221-5
Keywords
- Sierpinski gasket
- Kusuoka measure
- Riemannian structure
- Geodesic metric
- Heat kernel
- Short time asymptotics