Liouville theorems for ancient solutions of subexponential growth to the heat equation on graphs

Discrete potential theory (31C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Cites Work

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The Dirichlet problem at infinity for manifolds of negative curvature
The Dirichlet problem at infinity for a negatively curved manifold
Instability of Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains
On the parabolic kernel of the Schrödinger operator
Positive harmonic functions on complete manifolds with non-negative curvature outside a compact set
Harmonic functions on manifolds
Liouville property for groups and manifolds
Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition
Liouville theorem and coupling on negatively curved Riemannian manifolds.
A Liouville-type theorem for smooth metric measure spaces
Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs
A gradient estimate for positive functions on graphs
Optimal bounds for ancient caloric functions
Non-negative Ollivier curvature on graphs, reverse Poincaré inequality, Buser inequality, Liouville property, Harnack inequality and eigenvalue estimates
Instability of the Liouville property for quasi-isometric graphs and manifolds of polynomial volume growth
Li-Yau inequality on graphs
Dimension of spaces of harmonic functions
SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
Differential equations on riemannian manifolds and their geometric applications
Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
Introduction to Analysis on Graphs
Liouville theorems for ancient caloric functions via optimal growth conditions
Graphs and Discrete Dirichlet Spaces
On Ancient Solutions of the Heat Equation
Geometric analysis

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