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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:

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

20017 Alexander Grigor'yan, Rolando Jimenez, Yuri Muranov PDF

Homology of path complexes and hypergraphs

Project: A3

Published: Topology and its Applications 267, no. 106877 (2019)

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Homology of path complexes and hypergraphs


Authors: Alexander Grigor'yan, Rolando Jimenez, Yuri Muranov Projects: A3
Submission Date: 27.01.2020 Submitter: Moritz Kaßmann
Download: PDF Link: 20017
Published: Topology and its Applications 267, no. 106877 (2019)

20016 Alexander Grigor'yan, Jun Cao PDF

Heat kernels and Besov spaces associated with second order divergence form elliptic operators

Project: A3

Published: J. Fourier Anal. Appl. 26, no. 3 (2020)

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Heat kernels and Besov spaces associated with second order divergence form elliptic operators


Authors: Alexander Grigor'yan, Jun Cao Projects: A3
Submission Date: 27.01.2020 Submitter: Moritz Kaßmann
Download: PDF Link: 20016
Published: J. Fourier Anal. Appl. 26, no. 3 (2020)

20015 Alexander Grigor'yan, Yuhua Sun, Igor Verbitsky PDF

Superlinear elliptic inequalities on manifolds

Project: A3

To appear: J. Funct. Anal. (2020)

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Superlinear elliptic inequalities on manifolds


Authors: Alexander Grigor'yan, Yuhua Sun, Igor Verbitsky Projects: A3
Submission Date: 27.01.2020 Submitter: Moritz Kaßmann
Download: PDF Link: 20015
To appear: J. Funct. Anal. (2020)

20014 Alexander Grigor'yan, Rolando Jimenez, Yuri Muranov PDF

Cubical and path homology theories for digraphs

Project: A3

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Cubical and path homology theories for digraphs


Authors: Alexander Grigor'yan, Rolando Jimenez, Yuri Muranov Projects: A3
Submission Date: 27.01.2020 Submitter: Moritz Kaßmann
Download: PDF Link: 20014

20013 Alexander Grigor'yan, Jun Cao PDF

Heat kernels and Besov spaces on metric measure space

Project: A3

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Heat kernels and Besov spaces on metric measure space


Authors: Alexander Grigor'yan, Jun Cao Projects: A3
Submission Date: 27.01.2020 Submitter: Moritz Kaßmann
Download: PDF Link: 20013

19094 Shokoufe Faraji, Alexander Grigor'yan PDF

On biparabolicity of Riemannian manifolds

Project: A3

Published: Rev. Mat. Iberoam. 35 (2019), 2025-2034

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On biparabolicity of Riemannian manifolds


Authors: Shokoufe Faraji, Alexander Grigor'yan Projects: A3
Submission Date: 10.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19094
Published: Rev. Mat. Iberoam. 35 (2019), 2025-2034

19093 Alexander Grigor'yan, Eryan Hu, Jiaxin Hu PDF

Two sides estimates of heat kernels of jump type Dirichlet forms

Project: A3

Published: Advances in Math. 330 (2018), 433-515

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Two sides estimates of heat kernels of jump type Dirichlet forms


Authors: Alexander Grigor'yan, Eryan Hu, Jiaxin Hu Projects: A3
Submission Date: 10.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19093
Published: Advances in Math. 330 (2018), 433-515

19092 Alexander Grigor'yan, Yuri Kondratiev, Andrey Piatnitski, Elena Zhizhina PDF

Pointwise estimates for heat kernels of convolution-type operators

Project: A3

Published: Proc. LMS 117 (2018), 849-880

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Pointwise estimates for heat kernels of convolution-type operators


Authors: Alexander Grigor'yan, Yuri Kondratiev, Andrey Piatnitski, Elena Zhizhina Projects: A3
Submission Date: 10.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19092
Published: Proc. LMS 117 (2018), 849-880

19091 Alexander Grigor'yan, Igor Verbitsky PDF

Pointwise estimates of solutions to nonlinear equations for nonlocal operators

Project: A3

To appear: Ann. Scuola Norm. Sup. Pisa (2019)

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Pointwise estimates of solutions to nonlinear equations for nonlocal operators


Authors: Alexander Grigor'yan, Igor Verbitsky Projects: A3
Submission Date: 10.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19091
To appear: Ann. Scuola Norm. Sup. Pisa (2019)



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