Abstract
The spectral dimension and the Hausdorff dimension of the Sierpiński gasket are known to be different. Kigami proved that the Hausdorff dimension d h with respect to the harmonic metric is less than or equal to the spectral dimension and conjectured equality. We give estimates of d h which are strictly less than the spectral dimension and therefore disprove this conjecture.
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Teufl, E. (2003). On the Hausdorff Dimension of the Sierpiński Gasket with respect to the Harmonic Metric. In: Grabner, P., Woess, W. (eds) Fractals in Graz 2001. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8014-5_11
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DOI: https://doi.org/10.1007/978-3-0348-8014-5_11
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9403-6
Online ISBN: 978-3-0348-8014-5
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