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Cited by 99Geometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsGeometry and complex manifolds

Stability results for Harnack inequalities

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Grigor'yan, Alexander, Saloff-Coste, Laurent·2005·Annales de l'Institut Fourier
DOI 10.5802/aif.2116
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Abstract

We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically non-negative sectional curvature.

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  • The method employed in the proof of Lemma 2.2 is due to Grigoryan and Saloff-Coste in much greater generality.

    “The method employed in the proof of Lemma 2.2 is due to Grigoryan and Saloff-Coste [19] in much greater generality.”

    From Gravitational instantons from rational elliptic surfaces (2011) · cites this paper as [19]

    The Introduction (page unavailable) says Grigor’yan and Saloff-Coste provide methods for proving Harnack inequalities, and the overview describes a discretization technique. But the claim does not identify the method used in the citing paper’s Lemma 2.2, so our copy cannot establish that it is the same method or that this paper treats it in greater generality. Searched for the lemma number and descriptions of the proof method. (LLM, conf=0.70)

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Research works printed but not linked: 44

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Authors
Grigor'yan, A., & Saloff-Coste, L.
Affiliations
Imperial College London (GB)
ORCID
Grigor'yan, Alexander
Venue
Annales de l'Institut Fourier
Publisher
MathDoc/Centre Mersenne
Published
2005
Volume
55
Issue
3
Pages
825-890
ISSN
  • 0373-0956 (ISSN-L)
  • 1777-5310
DOI
10.5802/aif.2116
OpenAlex
W603813428
Cited by
99
References
0
Citations by year
2026: 3 · 2025: 7 · 2024: 4 · 2023: 4 · 2022: 6 · 2021: 6 · 2020: 4 · 2019: 9 · 2018: 8 · 2017: 6 · 2016: 2 · 2015: 9 · 2014: 3 · 2013: 1 · 2012: 3
FWCI
4.83
Type
journal article
Language
en
Open access
Locations
  • Annales de l’institut Fourier (publishedVersion)
  • Annals of the Fourier Institute (Institut Fourier) (submittedVersion)
  • French digital mathematics library (Numdam) (submittedVersion)
Funders
  • National Science Foundation (0102126, 9802855)
  • London Mathematical Society
  • Engineering and Physical Sciences Research Council
Topics
  • Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
  • Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Partial Differential Equations
  • Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
Keywords
Harnack inequality, weighted Riemannian manifolds, parabolic Harnack inequality, complete noncompact manifolds, nonnegative Ricci curvature

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