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Project A3: Analysis on manifolds, metric spaces and graphs


Principal Investigator(s)
Alexander Grigor'yan
Visitor(s)
Yannick Sire

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:

25050 Alexander Grigor'yan, Giulia Meglioli, Alberto Roncoroni PDF

Rigidity for the heat equation with density on Riemannian manifolds through a conformal change, submitted (2025)

Project: A3, A8

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Rigidity for the heat equation with density on Riemannian manifolds through a conformal change, submitted (2025)


Authors: Alexander Grigor'yan, Giulia Meglioli, Alberto Roncoroni Projects: A3, A8
Submission Date: 08.09.2025 Submitter: Giulia Meglioli
Download: PDF Link: 25050

24040 Alexander Grigor'yan, Philipp Sürig PDF

Sharp propagation rate for solutions of Leibenson's equation on Riemannian manifolds

Project: A3

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Sharp propagation rate for solutions of Leibenson's equation on Riemannian manifolds


Authors: Alexander Grigor'yan, Philipp Sürig Projects: A3
Submission Date: 06.06.2024 Submitter: Sebastian Herr
Download: PDF Link: 24040

24039 Alexander Grigor'yan, Philipp Sürig PDF

Upper bounds for solutions of Leibenson’s equation on Riemannian manifolds

Project: A3

To appear: Journal of Functional Analysis (2025)

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Upper bounds for solutions of Leibenson’s equation on Riemannian manifolds


Authors: Alexander Grigor'yan, Philipp Sürig Projects: A3
Submission Date: 06.06.2024 Submitter: Sebastian Herr
Download: PDF Link: 24039
To appear: Journal of Functional Analysis (2025)

24038 Alexander Grigor'yan, Yong Lin, Shing-Tung Yau, Haohang Zhang PDF

Eigenvalues of the Hodge Laplacian on digraphs

Project: A3

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Eigenvalues of the Hodge Laplacian on digraphs


Authors: Alexander Grigor'yan, Yong Lin, Shing-Tung Yau, Haohang Zhang Projects: A3
Submission Date: 07.06.2024 Submitter: Sebastian Herr
Download: PDF Link: 24038

24037 Alexander Grigor'yan, Leandro Pessoa, Alberto G. Setti PDF

$L^p$-parabolicity of Riemannian manifolds

Project: A3

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$L^p$-parabolicity of Riemannian manifolds


Authors: Alexander Grigor'yan, Leandro Pessoa, Alberto G. Setti Projects: A3
Submission Date: 06.06.2024 Submitter: Sebastian Herr
Download: PDF Link: 24037

24036 Alexander Grigor'yan, Eryan Hu, Jiaxin Hu PDF

Tail estimates and off-diagonal upper bounds of the heat kernel

Project: A3

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Tail estimates and off-diagonal upper bounds of the heat kernel


Authors: Alexander Grigor'yan, Eryan Hu, Jiaxin Hu Projects: A3
Submission Date: 06.06.2024 Submitter: Sebastian Herr
Download: PDF Link: 24036

23114 Alexander Grigor'yan PDF

Analysis on ultra-metric spaces via heat kernels

Project: A3

Published: p-Adic Numbers, Ultrametric Analysis and Applications 15 (2023), 204–242

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Analysis on ultra-metric spaces via heat kernels


Authors: Alexander Grigor'yan Projects: A3
Submission Date: 06.06.2024 Submitter: Sebastian Herr
Download: PDF Link: 23114
Published: p-Adic Numbers, Ultrametric Analysis and Applications 15 (2023), 204–242

23102 Philipp Sürig PDF

Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds

Project: A3

Published: Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal 249 (2024), Article number 113641

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Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds


Authors: Philipp Sürig Projects: A3
Submission Date: 29.12.2024 Submitter: Alexander Grigor'yan
Download: PDF Link: 23102
Published: Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal 249 (2024), Article number 113641

23006 Alexander Grigor'yan, Philipp Sürig PDF

Finite propagation speed for Leibenson’s equation on Riemannian manifolds

Project: A3

Published: Communications in Analysis and Geometry 32 (2024), 2467–2504

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Finite propagation speed for Leibenson’s equation on Riemannian manifolds


Authors: Alexander Grigor'yan, Philipp Sürig Projects: A3
Submission Date: 20.01.2023 Submitter: Sebastian Herr
Download: PDF Link: 23006
Published: Communications in Analysis and Geometry 32 (2024), 2467–2504

22096 Alexander Grigor'yan, Eryan Hu, Jiaxin Hu PDF

Off-diagonal lower estimates and Hölder regularity of the heat kernel

Project: A3

Published: Asian Journal of Mathematics 27 (2023), 675–770

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Off-diagonal lower estimates and Hölder regularity of the heat kernel


Authors: Alexander Grigor'yan, Eryan Hu, Jiaxin Hu Projects: A3
Submission Date: 20.01.2023 Submitter: Sebastian Herr
Download: PDF Link: 22096
Published: Asian Journal of Mathematics 27 (2023), 675–770


All Publications of this Project


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