Volume doubling measures and heat kernel estimates on self-similar sets

By 木上淳. 2009

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Heat Kernel Asymptotics for the Measurable Riemannian Structure on the Sierpinski Gasket (2012, methodology): “First we introduce basic notions and results concerning the description of geometry of K, following [24].”
Estimates of heat kernels for non-local regular Dirichlet forms (2014, background): “the definition at the beginning of Section 6 as well as [27], [28], [29]).”
TWO-SIDED ESTIMATES OF HEAT KERNELS ON METRIC MEASURE SPACES (2012, background): “4 ) was proved by Barlow and Perkins [12] on SG, by Kumagai [48] on nested fractals, by Fitzsimmons, Hambly and Kumagai [19] on affine nested fractals and by Barlow and Bass on SC [4] and on generalized Sierpinski carpets [5] (see also [2, 7, 44, 47, 50]).”
Spectral asymptotics for Laplacians on self-similar sets (2010, methodology): “The first two statements follow from Kigami [28, Proof of Theorem 1.2.7], but we include the proof for ease of the reading.”