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Project A3: Analysis on manifolds, metric spaces and graphs


Principal Investigator(s)
Alexander Grigor'yan
Visitor(s)
Currently no visitors.

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.


Recent Preprints:

20089 Shilei Kong, Ka-Sing Lau, Jun Jason Luo, Xiang-Yang Wang PDF

Hyperbolic graphs induced by iterations and applications in fractals

Project: A3

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Hyperbolic graphs induced by iterations and applications in fractals


Authors: Shilei Kong, Ka-Sing Lau, Jun Jason Luo, Xiang-Yang Wang Projects: A3
Submission Date: 26.07.2020 Submitter: Alexander Grigor'yan
Download: PDF Link: 20089

20088 Shilei Kong, Ka-Sing Lau, Xiang-Yang Wang PDF

Gromov hyperbolic graphs arising from iterations

Project: A3

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Gromov hyperbolic graphs arising from iterations


Authors: Shilei Kong, Ka-Sing Lau, Xiang-Yang Wang Projects: A3
Submission Date: 26.07.2020 Submitter: Alexander Grigor'yan
Download: PDF Link: 20088

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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Random walks and induced Dirichlet forms on compact spaces of homogeneous type


Authors: Shilei Kong, Ka-Sing Lau, Ting-Kam Leonard Wong Projects: A3
Submission Date: 26.07.2020 Submitter: Alexander Grigor'yan
Download: PDF Link: 20087
Published: Analysis, Probability and Mathematical Physics on Fractals, eds. P. A. Ruiz et al., World Scientific, Singapore (2020), 273–296

20086 Alexander Grigor'yan PDF

Analysis on manifolds and volume growth

Project: A3

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Analysis on manifolds and volume growth


Authors: Alexander Grigor'yan Projects: A3
Submission Date: 26.07.2020 Submitter: Sebastian Herr
Download: PDF Link: 20086

20085 Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov PDF

Hierarchical Schrödinger type operators: the case of potentials with local singularities

Project: A3

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Hierarchical Schrödinger type operators: the case of potentials with local singularities


Authors: Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov Projects: A3
Submission Date: 26.07.2020 Submitter: Sebastian Herr
Download: PDF Link: 20085

20084 Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov PDF

Hierarchical Schrödinger type operators: the case of locally bounded potentials

Project: A3

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Hierarchical Schrödinger type operators: the case of locally bounded potentials


Authors: Alexander Bendikov, Alexander Grigor'yan, Stanislav Molchanov Projects: A3
Submission Date: 26.07.2020 Submitter: Sebastian Herr
Download: PDF Link: 20084

20083 Jun Cao, Alexander Grigor'yan, Liguang Liu PDF

Hardy’s inequality and Green function on metric measure spaces

Project: A3

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Hardy’s inequality and Green function on metric measure spaces


Authors: Jun Cao, Alexander Grigor'yan, Liguang Liu Projects: A3
Submission Date: 26.07.2020 Submitter: Sebastian Herr
Download: PDF Link: 20083

20082 Alexander Grigor'yan, Eryan Hu, Jiaxin Hu PDF

The pointwise existence and properties of heat kernel

Project: A3

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The pointwise existence and properties of heat kernel


Authors: Alexander Grigor'yan, Eryan Hu, Jiaxin Hu Projects: A3
Submission Date: 26.07.2020 Submitter: Sebastian Herr
Download: PDF Link: 20082

20064 Simon Noah Nowak PDF

Higher Hölder regularity for nonlocal equations with irregular kernel

Project: A3

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Higher Hölder regularity for nonlocal equations with irregular kernel


Authors: Simon Noah Nowak Projects: A3
Submission Date: 27.06.2020 Submitter: Alexander Grigor'yan
Download: PDF Link: 20064

20018 Wolfhard Hansen, Ivan Netuka PDF

On Evans' and Choquet's theorems for polar sets

Project: A3

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On Evans' and Choquet's theorems for polar sets


Authors: Wolfhard Hansen, Ivan Netuka Projects: A3
Submission Date: 30.01.2020 Submitter: Alexander Grigor'yan
Download: PDF Link: 20018



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