Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka measure and the Gaussian heat kernel estimate
By Jun Kigami. 2008
86 citations recorded by the source corpus.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/fcad72f8d3aa4fd9a22f047195716327388b9611
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Pekka Koskela
- Yuan Zhou
- Fabrice Baudoin
- Alexander Teplyaev
- Nageswari Shanmugalingam
- Mathav Kishore Murugan
- Michael Hinz
- Naotaka Kajino
In Geometry and Topology
- Yuan Zhou
- Pekka Koskela
- Naotaka Kajino
- Patricia Alonso-Ruiz
- Luke G. Rogers
- Fabrice Baudoin
- Li Chen
- Alexander Teplyaev
Citations in the corpus
- Geometry and Analysis of Dirichlet forms (2012, background): “2, and all the properties needed in the arguments are available by [22, 24, 19].”
- Developments in fractal geometry (2013, unknown): “Analysis on fractals involves the construction of Laplacians [73], harmonic analysis, Brownian motion [12], heat kernels [77] (see the review in [74]), and differential equations on fractals [117].”
- Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, background): “In the context of fractals, strictly local Dirichlet forms appear in [4, 23, 24, 34, 47, 54,55,58,61,68,76, 91,92] and play an important role in analysis of first-order derivatives in these settings.”
- Stability of elliptic Harnack inequality (2016, background): “15(c) to obtain PHI(2). A paper in preparation [KM] shows that this is not possible in general, but on the other hand the Sierpinski gasket provides a non-trivial example where this is possible – see [Ki1]. See [Kaj, Section 9] for further discussion on this problem. (3) The constant β>0 in Theor”
- Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces (2012, background): “Harmonic coordinates in the sense of [36, 39, 63] constitute a prototype example.”
- Heat Kernel Asymptotics for the Measurable Riemannian Structure on the Sierpinski Gasket (2012, methodology): “In Section 3 we briefly recall the results of [25] on the volume doubling property of the Kusuoka measure and basics on the harmonic geodesic metric, with slight improvements.”