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Partial Differential Equations;Geometry

In this talk we will discuss a new geodesic beam approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of $L^{2}$ mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Using the description of concentration, we obtain quantitative improvements on the known bounds in a wide variety of settings. In this talk we will discuss a new geodesic beam approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of $L^{2}$ mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along ...

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Documents 53C21 | enregistrements trouvés : 100

Understanding the growth of Laplace eigenfunctions (part 1 of 2) Canzani, Yaiza | CIRM H Nouveau

Topics in differential geometry. Vol. 2 :a colloquia on... held in debrecen Aug. 26 - Sept. 1 Szenthe, J. ; Tamassy, L. | North-Holland Publisher House 1988 Nouveau

New developments in differential geometryproceedings of the colloquium on differential geometryJuly 26-30 Szenthe, J. ; Tamassy, L. | Kluwer Academic Publishers 1996 Nouveau

Structure transverse des feuilletages,toulouse,17-19 fevrier 1982 Pradines, J. | S.M.F. 1984 Nouveau

Geometric analysis : partial differential equations and surfaces:UIMP-RSME Lluis Santalo Summer School 2010: geometric analysis,June 28-July 2, 2010#University of Granada, Spain Pérez, Joaquin ; Galvez, José A. | American Mathematical Society 2012 Nouveau

Concentration, functional inequalities and isoperimetry.International workshop on concentration, functional inequalities and isoperimetryBoca Raton # october 29-november 1, 2009 Houdré, Christian ; Ledoux, Michel ; Milman, Emanuel ; Milman, Mario | American Mathematical Society 2011 Nouveau

Global riemannian geometryproceedings of the symposium on global riemannian geometry held at the university of durham,july 1983 Hitchin, N. J. ; Willmore, T. J. | Ellis Horwood Ltd;John Wiley And Sons 1984 Nouveau

Analysis and geometry of metric measure spaces:lecture notes of the 50th séminaire de mathématiques supérieures (SMS)Montréal # june 27- july 8, 2011 Dafni, Galia ; McCann, Robert John ; Stancu, Alina | American Mathematical Society 2013 Nouveau

Differential geometryproceedings of the first international symposium on ... Feb.22-24 Cheng, Qing-Ming | Graduate School of Science;Josai University 2001 Nouveau

Geometric evolution equations :national center for theoretical sciences workshop on...#July 15-Aug. 14 Chang, Shu-Cheng ; Chow, Bennett ; Chu, Sun-Chin ; Lin, Chang-Shou | American Mathematical Society 2005 Nouveau

Surveys in differential geometry 2013. Vol. XVIII:geometry and topology.Lectures given at the geometry and topology conferencesCambridge # april 29 - may 1, 2011Bethlehem # may 25-27, 2012 Cao, Huai-Dong ; Yau, Shing-Tung | International Press 2013 Nouveau

Geometric aspects of partial differential equations :proceedings of a minisymposium on spectral invariants, heat equation approach#Sept. 18-19 Booss-Bavnbek, Bernhelm ; Wojciechowski, Krzysztof | American Mathematical Society 1999 Nouveau

Géométries à courbure négative ou nulle, groupes discrets et rigiditésGrenoble # 2004 Bessières, L. ; Parreau, Anne ; Rémy, Bertrand | Société Mathématique de France 2009 Nouveau

Fractal geometry and analysisproceedings of the NATO advanced study institute and séminaire de mathématiques supérieures on ...July 3-21 Bélair, Jacques ; Dubuc, Serge | Kluwer Academic Publishers 1991 Nouveau

Analytic aspects of problems in Riemannian geometry: elliptic PDEs, solitons and computer imagingLandéda # may 9-13, 2005 Baird, Paul ; El Soufi, A. ; Fardoun, A. ; Regbaoui, R. | Société Mathématique de France 2011 Nouveau

Geometry, topology, and dynamics in negative curvature.Proceedings of the ICM 2010 satellite conferenceBangalore # August 2-7, 2010 Aravinda, C. S. ; Farrell, F. Thomas ; Lafont, Jean-François | Cambridge University Press 2016 Nouveau

Proceedings of the Gökova geometry-topology conference 2010 Akbulut, Selman ; Auroux, Denis ; Onder, Turgut | International Press;Gökova geometry-topology conferences 2010 Nouveau

Proceedings of the international conference on prospects in mathematicsresearch institute for mathematical sciences#April 18-23 | Kyoto University 1974 Nouveau

Global analysis and its applications. Vol. 1lectures presented at an international seminar courseJuly 4 - Aug. 25 | Internationl Atomic Energy Agency 1974 Nouveau

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Topics in differential geometry. Vol. 2 :
a colloquia on... held in debrecen Aug. 26 - Sept. 1 Szenthe, J. ; Tamassy, L. | North-Holland Publisher House 1988 Nouveau

New developments in differential geometry
proceedings of the colloquium on differential geometry
July 26-30 Szenthe, J. ; Tamassy, L. | Kluwer Academic Publishers 1996 Nouveau

Geometric analysis : partial differential equations and surfaces:
UIMP-RSME Lluis Santalo Summer School 2010: geometric analysis,
June 28-July 2, 2010#
University of Granada, Spain Pérez, Joaquin ; Galvez, José A. | American Mathematical Society 2012 Nouveau

Concentration, functional inequalities and isoperimetry.
International workshop on concentration, functional inequalities and isoperimetry
Boca Raton # october 29-november 1, 2009 Houdré, Christian ; Ledoux, Michel ; Milman, Emanuel ; Milman, Mario | American Mathematical Society 2011 Nouveau

Global riemannian geometry
proceedings of the symposium on global riemannian geometry held at the university of durham,july 1983 Hitchin, N. J. ; Willmore, T. J. | Ellis Horwood Ltd;John Wiley And Sons 1984 Nouveau

Analysis and geometry of metric measure spaces:
lecture notes of the 50th séminaire de mathématiques supérieures (SMS)
Montréal # june 27- july 8, 2011 Dafni, Galia ; McCann, Robert John ; Stancu, Alina | American Mathematical Society 2013 Nouveau

Differential geometry
proceedings of the first international symposium on ...
Feb.22-24 Cheng, Qing-Ming | Graduate School of Science;Josai University 2001 Nouveau

Geometric evolution equations :
national center for theoretical sciences workshop on...#July 15-Aug. 14 Chang, Shu-Cheng ; Chow, Bennett ; Chu, Sun-Chin ; Lin, Chang-Shou | American Mathematical Society 2005 Nouveau

Surveys in differential geometry 2013. Vol. XVIII:
geometry and topology.
Lectures given at the geometry and topology conferences
Cambridge # april 29 - may 1, 2011
Bethlehem # may 25-27, 2012 Cao, Huai-Dong ; Yau, Shing-Tung | International Press 2013 Nouveau

Geometric aspects of partial differential equations :
proceedings of a minisymposium on spectral invariants, heat equation approach#Sept. 18-19 Booss-Bavnbek, Bernhelm ; Wojciechowski, Krzysztof | American Mathematical Society 1999 Nouveau

Géométries à courbure négative ou nulle, groupes discrets et rigidités
Grenoble # 2004 Bessières, L. ; Parreau, Anne ; Rémy, Bertrand | Société Mathématique de France 2009 Nouveau

Fractal geometry and analysis
proceedings of the NATO advanced study institute and séminaire de mathématiques supérieures on ...
July 3-21 Bélair, Jacques ; Dubuc, Serge | Kluwer Academic Publishers 1991 Nouveau

Analytic aspects of problems in Riemannian geometry: elliptic PDEs, solitons and computer imaging
Landéda # may 9-13, 2005 Baird, Paul ; El Soufi, A. ; Fardoun, A. ; Regbaoui, R. | Société Mathématique de France 2011 Nouveau

Geometry, topology, and dynamics in negative curvature.
Proceedings of the ICM 2010 satellite conference
Bangalore # August 2-7, 2010 Aravinda, C. S. ; Farrell, F. Thomas ; Lafont, Jean-François | Cambridge University Press 2016 Nouveau

Proceedings of the international conference on prospects in mathematics
research institute for mathematical sciences#April 18-23 | Kyoto University 1974 Nouveau

Global analysis and its applications. Vol. 1
lectures presented at an international seminar course
July 4 - Aug. 25 | Internationl Atomic Energy Agency 1974 Nouveau