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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:

19094 Shokoufe Faraji, Alexander Grigor'yan PDF

On biparabolicity of Riemannian manifolds

Project: A3

To appear: Rev. Mat. Iberoam. (2019)

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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
To appear: Rev. Mat. Iberoam. (2019)

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)

19090 Alexander Grigor'yan, Satoshi Ishiwata, Laurent Saloff-Coste PDF

Heat kernel estimates on connected sums of parabolic manifolds

Project: A3

Published: J. Math. Pures Appl. 113 (2018), 155-194

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Heat kernel estimates on connected sums of parabolic manifolds


Authors: Alexander Grigor'yan, Satoshi Ishiwata, Laurent Saloff-Coste Projects: A3
Submission Date: 10.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19090
Published: J. Math. Pures Appl. 113 (2018), 155-194

19089 Alexander Grigor'yan, Yuri Muranov, Vladimir Vershinin, Shing-Tung Yau PDF

Path homology theory of multigraphs and quivers

Project: A3

Published: Forum Math. 30 (2018), 1319-1337

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Path homology theory of multigraphs and quivers


Authors: Alexander Grigor'yan, Yuri Muranov, Vladimir Vershinin, Shing-Tung Yau Projects: A3
Submission Date: 10.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19089
Published: Forum Math. 30 (2018), 1319-1337

19088 Alexander Grigor'yan, Yuhua Sun PDF

On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds

Project: A3

To appear: Calc. Var. PDEs (2019)

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On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds


Authors: Alexander Grigor'yan, Yuhua Sun Projects: A3
Submission Date: 10.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19088
To appear: Calc. Var. PDEs (2019)

19087 Alexander Bendikov, Alexander Grigor'yan, Eryan Hu, Jiaxin Hu PDF

Heat kernels and non-local Dirichlet forms on ultra-metric spaces

Project: A3

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Heat kernels and non-local Dirichlet forms on ultra-metric spaces


Authors: Alexander Bendikov, Alexander Grigor'yan, Eryan Hu, Jiaxin Hu Projects: A3
Submission Date: 10.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19087

19062 Simon Noah Nowak PDF

$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations

Project: A3

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$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations


Authors: Simon Noah Nowak Projects: A3
Submission Date: 24.07.2019 Submitter: Alexander Grigor'yan
Download: PDF Link: 19062

19031 Simon Noah Nowak PDF

$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations

Project: A3

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$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations


Authors: Simon Noah Nowak Projects: A3
Submission Date: 14.06.2019 Submitter: Alexander Grigor'yan
Download: PDF Link: 19031



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