Dirac operators and geodesic metric on the harmonic Sierpiński gasket and other fractal sets

DOI10.4171/JNCG/174zbMath1320.28015arXiv1212.0878MaRDI QIDQ2264066

Jonathan J. Sarhad, Michel L. Lapidus

Publication date: 20 March 2015

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.0878

zbMATH Keywords

spectral dimensionspectral triplesanalysis on fractalsfractal manifoldEuclidean and harmonic Sierpiński gasketsfractals built on curvesgeodesic and noncommutative metricsgeodesics on fractalsgeometric analysis on fractalsLaplacians and Dirac operators on fractalsmeasurable Riemannian geometrynoncommutative fractal geometry

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Spin and Spin({}^c) geometry (53C27) Noncommutative geometry in quantum theory (81R60) Fractals (28A80) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Noncommutative geometry (à la Connes) (58B34) Local Riemannian geometry (53B20) Methods of local Riemannian geometry (53B21) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (13)

On the packing measure of the Sierpinski gasket ⋮ Isometry groups of inductive limits of metric spectral triples and Gromov–Hausdorff convergence ⋮ Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis ⋮ Unnamed Item ⋮ Convergence of inductive sequences of spectral triples for the spectral propinquity ⋮ Dual graphs and modified Barlow-Bass resistance estimates for repeated barycentric subdivisions ⋮ Examples of infinite direct sums of spectral triples ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Spectral triples and wavelets for higher-rank graphs ⋮ A spectral triple for a solenoid based on the Sierpinski gasket ⋮ Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back ⋮ Spectral triples for the variants of the Sierpiński gasket

Cites Work

• Sums of two-dimensional spectral triples
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