Analysis and geometry of the measurable Riemannian structure on the Sierpi nski gasket

  title={Analysis and geometry of the measurable Riemannian structure on the Sierpi nski gasket},
  author={Naotaka Kajino},
This expository article is devoted to a survey of existent results concerning the measurable Riemannian structure on the Sierpi� nski gasket and to a brief account of the author's recent result on Weyl's eigenvalue asymptotics of its associated Laplacian. In particular, properties of the Hausdorff measure with respect to the canonical geodesic metric are described in some detail as a key step to the proof of Weyl's asymptotics. A complete characterization of minimal geodesics is newly proved… 

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