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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 56
  3. Calculus of Variations and Partial Differential Equations : Volume 56, Issue 1, February 2017
  4. Remarks on curvature dimension conditions on graphs
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 56, Issue 3, June 2017
Calculus of Variations and Partial Differential Equations : Volume 56, Issue 2, April 2017
Calculus of Variations and Partial Differential Equations : Volume 56, Issue 1, February 2017
Remarks on curvature dimension conditions on graphs
Hölder continuity for continuous solutions of the singular minimal surface equation with arbitrary zero set
A necessary condition for lower semicontinuity of line energies
Grand p-harmonic energy
Radó–Kneser–Choquet theorem for harmonic mappings between surfaces
Spectral density estimates with partial symmetries and an application to Bahri–Lions-type results
Fractional capacities relative to bounded open Lipschitz sets complemented
Combining linear and fast diffusion in a nonlinear elliptic equation
Minimisers of the Allen–Cahn equation on hyperbolic graphs
Deformation concentration for martensitic microstructures in the limit of low volume fraction
Absolutely minimising generalised solutions to the equations of vectorial calculus of variations in $$L^\infty $$
On local behavior of singular positive solutions to nonlocal elliptic equations
Localized nodal solutions of higher topological type for semiclassical nonlinear Schrödinger equations
Higher regularity of the free boundary in the parabolic Signorini problem
Partial regularity and smooth topology-preserving approximations of rough domains
On perturbations of the fractional Yamabe problem
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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Remarks on curvature dimension conditions on graphs

Content Provider SpringerLink
Author Münch, Florentin
Copyright Year 2017
Abstract We show a connection between the $$CDE'$$ inequality introduced in Horn et al. (Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for nonnegative curvature graphs. arXiv:1411.5087v2 , 2014) and the $$CD\psi $$ inequality established in Münch (Li–Yau inequality on finite graphs via non-linear curvature dimension conditions. arXiv:1412.3340v1 , 2014). In particular, we introduce a $$CD_\psi ^\varphi $$ inequality as a slight generalization of $$CD\psi $$ which turns out to be equivalent to $$CDE'$$ with appropriate choices of $$\varphi $$ and $$\psi $$ . We use this to prove that the $$CDE'$$ inequality implies the classical CD inequality on graphs, and that the $$CDE'$$ inequality with curvature bound zero holds on Ricci-flat graphs.
Ending Page 8
Page Count 8
Starting Page 1
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 1
Volume Number 56
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2017-01-07
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Heat equation Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Methods of Riemannian geometry, including PDE methods; curvature restrictions Random walks on graphs
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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