Minimisers of the Allen-Cahn equation on hyperbolic graphs

DOI10.1007/s00526-016-1100-xzbMath1368.58008arXiv1601.06271OpenAlexW3105528599WikidataQ115387314 ScholiaQ115387314MaRDI QIDQ522456

Blaž Mramor

Publication date: 13 April 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06271

zbMATH Keywords

hyperbolic graphAllen-Cahn equationdiscrete Laplace operatorminimisers

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Variational methods for second-order elliptic equations (35J20)

Related Items (1)

Minimisers of the Allen-Cahn equation on hyperbolic graphs

Cites Work

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• Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces of finite total curvature in \(\mathbb{R}^3\)
• Minimisers of the Allen-Cahn equation on hyperbolic graphs
• The Dirichlet problem at infinity for manifolds of negative curvature
• The Dirichlet problem at infinity for a negatively curved manifold
• The density at infinity of a discrete group of hyperbolic motions
• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• On the Aubry-Mather theory in statistical mechanics
• Patterson-Sullivan measures on the boundary of a hyperbolic space in the sense of Gromov
• Aubry-Mather theory for functions on lattices
• Embeddings of Gromov hyperbolic spaces
• Lectures on analysis on metric spaces
• The gradient theory of phase transitions and the minimal interface criterion
• Regularity of flat level sets in phase transitions
• Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces
• The ergodic theory of hyperbolic groups
• Phase Transitions and Minimal Hypersurfaces in Hyperbolic Space
• Multiple-layer solutions to the Allen-Cahn equation on hyperbolic space
• Asymptotic Dirichlet Problems for Harmonic Functions on Riemannian Manifolds
• Symmetry for solutions of two-phase semilinear elliptic equations on hyperbolic space
• On De Giorgi’s conjecture and beyond

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