Heat kernel asymptotics for the measurable Riemannian structure on the Sierpinski gasket
From MaRDI portal
Publication:658569
DOI10.1007/s11118-011-9221-5zbMath1248.28012OpenAlexW2105646148WikidataQ115381433 ScholiaQ115381433MaRDI QIDQ658569
Publication date: 12 January 2012
Published in: Potential Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11118-011-9221-5
potential theoryheat kernel estimatesfractal geometrygrowth of eigenvalues of the LaplacianRiemannian structures on fractals
Dirichlet forms (31C25) Fractals (28A80) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Transition functions, generators and resolvents (60J35)
Related Items
The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: a survey of the analytic aspects ⋮ Indices of Dirichlet forms ⋮ Hausdorff dimensions for graph-directed measures driven by infinite rooted trees ⋮ Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates ⋮ On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions ⋮ Estimates of the Local Spectral Dimension of the Sierpinski Gasket ⋮ Dual graphs and modified Barlow-Bass resistance estimates for repeated barycentric subdivisions ⋮ Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces ⋮ Random Walks on Barycentric Subdivisions and the Strichartz Hexacarpet ⋮ Geometry and analysis of Dirichlet forms ⋮ Geodesic distances and intrinsic distances on some fractal sets ⋮ Sup-norm-closable bilinear forms and Lagrangians ⋮ Higher order Laplacians on p.c.f. fractals with three boundary points and dihedral symmetry ⋮ Approximation of partial differential equations on compact resistance spaces ⋮ The Kusuoka measure and the energy Laplacian on level-\(k\) Sierpiński gaskets ⋮ Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals ⋮ Discrete approximations of metric measure spaces of controlled geometry
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Comparison inequalities for heat semigroups and heat kernels on metric measure spaces
- Spectral asymptotics for Laplacians on self-similar sets
- Dirichlet forms of fractals and products of random matrices
- On the parabolic kernel of the Schrödinger operator
- Brownian motion on the Sierpinski gasket
- Transition densities for Brownian motion on the Sierpinski carpet
- Dirichlet forms and analysis on Wiener space
- Differentiability of Lipschitz functions on metric measure spaces
- Estimates of transition densities for Brownian motion of nested fractals
- Dirichlet forms and symmetric Markov processes
- Transition density estimates for Brownian motion on affine nested fractals
- Short time asymptotic behaviour and large deviation for Brownian motion on some affine nested fractals
- Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds
- Small-time Gaussian behavior of symmetric diffusion semigroups
- Superposition operators on Dirichlet spaces
- Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
- Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
- Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka measure and the Gaussian heat kernel estimate
- Short-time asymptotics in Dirichlet spaces
- Resistance forms, quasisymmetric maps and heat kernel estimates
- Harmonic Coordinates on Fractals with Finitely Ramified Cell Structure
- Volume doubling measures and heat kernel estimates on self-similar sets
- Brownian Motion and Harmonic Analysis on Sierpinski Carpets
- Real Analysis and Probability
- Time changes of local Dirichlet spaces by energy measures of harmonic functions
- Diffusion processes in a small time interval
- Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractals
- Transition density asymptotics for some diffusion processes with multi-fractal structures
