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Summary:
The project A3 is concerned with properties of certain differential and non-local operators on manifolds, metric measure spaces, and graphs. The emphasis is made on the relationship between the analytic properties of the operators in question and the geometric properties of the underlying space. Examples of such properties include heat kernel estimates, existence of solutions of linear and non-linear PDEs in certain function classes, estimates of the eigenvalues of Hodge Laplacians, Schrödinger operators, etc.
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21024
Simon Noah Nowak PDF
Regularity theory for nonlocal equations with VMO coefficients Project: A3 Published: Ann. Inst. H. Poincaré C Anal. Non Linéaire 40, no. 1 (2023), 61–132 |
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21006
Shilei Kong, Ka-Sing Lau, Xiang-Yang Wang PDF
Near-isometries of hyperbolic graphs and bi-Lipschitz embeddings of their boundaries Project: A3 |
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20089
Shilei Kong, Ka-Sing Lau, Jun Jason Luo, Xiang-Yang Wang PDF
Hyperbolic graphs induced by iterations and applications in fractals Project: A3 Published: Analysis and partial differential equations on manifolds, fractals and graphs (2021), 143–181 Notes: Adv. Anal. Geom., 3 |
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20088
Shilei Kong, Ka-Sing Lau, Xiang-Yang Wang PDF
Gromov hyperbolic graphs arising from iterations Project: A3 Published: Adv. Math. 389, no. 107908 (2017), 38 pp |
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20087
Shilei Kong, Ka-Sing Lau, Ting-Kam Leonard Wong PDF
Random walks and induced Dirichlet forms on compact spaces of homogeneous type Project: A3 Published: Analysis, Probability and Mathematical Physics on Fractals, eds. P. A. Ruiz et al., World Scientific, Singapore (2020), 273–296 |
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20086
Alexander Grigor'yan PDF
Analysis on manifolds and volume growth Project: A3 Published: Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs (2021), 299–324 |
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20085
Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov PDF
Hierarchical Schrödinger type operators: the case of potentials with local singularities Project: A3 Published: Proc. Steklov Inst. Math. 323 (2023), 12–46. |
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20084
Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov PDF
Hierarchical Schrödinger type operators: the case of locally bounded potentials Project: A3 Published: Operator theory and harmonic analysis—OTHA 2020. Part II. Probability-analytical models, methods and applications (2021), 43–89 |
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20083
Jun Cao, Alexander Grigor'yan, Liguang Liu PDF
Hardy’s inequality and Green function on metric measure spaces Project: A3 Published: Journal of Functional Analysis 281, no. 3 (2021), Article No. 109020: 78 pp. |
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20082
Alexander Grigor'yan, Eryan Hu, Jiaxin Hu PDF
The pointwise existence and properties of heat kernel Project: A3 Published: Analysis and partial differential equations on manifolds, fractals and graphs (2021), 27–70 |
