Linear and Nonlinear Harmonic Boundaries of Graphs; An Approach with ℓ p-Cohomology in Degree One

DOI10.1007/978-3-030-56409-4_3OpenAlexW3108615620MaRDI QIDQ3384285

Antoine Gournay

Publication date: 15 December 2021

Published in: Frontiers in Analysis and Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-56409-4_3

zbMATH Keywords

\(\ell^p\)-cohomology in degree one

Mathematics Subject Classification ID

Cohomology of groups (20J06) Graph theory (05C99) Potential theory on Riemannian manifolds and other spaces (31C12)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Absence of non-constant harmonic functions with \(\ell^p\)-gradient in some semi-direct products
• Graphs of bounded degree and the \(p\)-harmonic boundary
• Oded Schramm: from circle packing to SLE
• Contracting automorphisms and \(L^p\)-cohomology in degree one
• Rough isometries, and combinatorial approximations of geometries of non- compact Riemannian manifolds
• Distortion of mappings and \(L_{q,p}\)-cohomology
• Boundary values, random walks, and \(\ell^p\)-cohomology in degree one
• Vanishing of the first reduced cohomology with values in an \(L^p\)-representation
• \(L_ 2\)-cohomology and group cohomology
• Instability of Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Parabolic and hyperbolic infinite networks
• Group cohomology, harmonic functions and the first \(L^ 2\)-Betti number
• Coarse cohomology and \(l_p\)-cohomology
• \(p\)-harmonic functions on graphs and manifolds
• Quasisymmetric parametrizations of two-dimensional metric spheres
• Introduction to \(\ell_2\)-methods in topology: Reduced \(\ell_2\)-homology, harmonic chains, \(\ell_2\)-Betti numbers
• Parabolicity of manifolds
• Conformal Assouad dimension and modulus
• \(\ell^2\) invariants of equivalence relations and groups
• Floyd maps for relatively hyperbolic groups.
• On the separation profile of infinite graphs
• Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups.
• Quasi-isometric invariance of continuous group \(L^p\)-cohomology, and first applications to vanishings
• Averages and the \(\ell^{q,1}\) cohomology of Heisenberg groups
• On the \(\ell ^{q,p}\) cohomology of Carnot groups
• Some applications of \(\ell_p\)-cohomology to boundaries of Gromov hyperbolic spaces
• On the first \(L^p\)-cohomology of discrete groups.
• The first \(L^p\)-cohomology of some groups with one end
• Orlicz spaces and the large scale geometry of Heintze groups
• Mixing, malnormal subgroups and cohomology in degree one
• \(L^p\)-cohomology and pincing
• Vanishing and non-vanishing for the first \(L^p\)-cohomology of groups.
• The first \(L^{p}\)-cohomology of some finitely generated groups and \(p\)-harmonic functions
• Harmonic functions with finite \(p\)-energy on lamplighter graphs are constant
• \(L^p\)-cohomology in degree 1 of homogeneous spaces
• \(L_{p, q}\)-cohomology and normal solvability
• Conditionally negative type functions on groups acting on regular trees
• On acylindrical hyperbolicity of groups with positive first ℓ²-Betti number
• L2-Betti Numbers and Non-Unitarizable Groups without Free Subgroups
• Cohomologie ℓp espaces de Besov
• Free Subgroups of Groups with Nontrivial Floyd Boundary
• Group Cohomology and L^p-Cohomology of Finitely Generated Groups
• LACK OF SPHERE PACKING OF GRAPHS VIA NONLINEAR POTENTIAL THEORY
• Lamplighter graphs do not admit harmonic functions of finite energy
• Random Walks on Infinite Graphs and Groups
• Vanishing of ℓ^p-cohomology and transportation cost

This page was built for publication: Linear and Nonlinear Harmonic Boundaries of Graphs; An Approach with ℓ p-Cohomology in Degree One