hangzhou lectures on eigenfunctions of the laplacian am 188 annals of mathematics studies

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Hangzhou Lectures On Eigenfunctions Of The Laplacian Am 188

Author : Christopher D. Sogge
ISBN : 9781400850549
Genre : Mathematics
File Size : 23. 19 MB
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Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic. Sogge begins with a treatment of the Hadamard parametrix before proving the first main result, the sharp Weyl formula. He avoids the use of Tauberian estimates and instead relies on sup-norm estimates for eigenfunctions. The author also gives a rapid introduction to the stationary phase and the basics of the theory of pseudodifferential operators and microlocal analysis. These are used to prove the Duistermaat-Guillemin theorem. Turning to the related topic of quantum ergodicity, Sogge demonstrates that if the long-term geodesic flow is uniformly distributed, most eigenfunctions exhibit a similar behavior, in the sense that their mass becomes equidistributed as their frequencies go to infinity.

Geometric Analysis

Author : Hubert L. Bray
ISBN : 9781470423131
Genre : Geometric analysis
File Size : 49. 89 MB
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This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

Spectral Theory And Partial Differential Equations

Author : James V Ralston
ISBN : 9781470409890
Genre : Differential equations, Partial
File Size : 26. 27 MB
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This volume contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held from June 17-21, 2013, at the University of California, Los Angeles, California, in honor of James Ralston's 70th Birthday. Papers in this volume cover important topics in spectral theory and partial differential equations such as inverse problems, both analytical and algebraic; minimal partitions and Pleijel's Theorem; spectral theory for a model in Quantum Field Theory; and beams on Zoll manifolds.

Hangzhou Lectures On Eigenfunctions Of The Laplacian

Author : Christopher Donald Sogge
ISBN : 0691160759
Genre : Mathematics
File Size : 79. 6 MB
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Contains the material taught during a series of lectures given at Zhejiang University in Hangzhou between 2010 and 2012.

Das Mathebuch

Author : Clifford A. Pickover
ISBN : 9089982809
Genre :
File Size : 50. 13 MB
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Function Spaces Differential Operators And Nonlinear Analysis

Author : Prof. Dr. Hans-Jürgen Schmeisser
ISBN : 9783663113362
Genre : Technology & Engineering
File Size : 23. 53 MB
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Analysis 2

Author : Otto Forster
ISBN : 9783322919083
Genre : Mathematics
File Size : 53. 13 MB
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Der vorliegende Band stellt den zweiten Teil eines Analysis-Kurses für Studierende der Mathematik und Physik dar. Das erste Kapitel über Differentialrechnung im R^n behandelt nach einer Einführung in die topologischen Grundbegriffe Kurven im R^n, partielle Ableitungen, totale Differenzierbarkeit, Taylorsche Formel, Maxima und Minima von Funktionen mehrerer Veränderlichen, implizite Funktionen und parameterabhängige Integrale. Das zweite Kapitel gibt eine kurze Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Nach dem Beweis des allgemeinen Existenz- und Eindeutigkeitssatzes und der Besprechung der Methode der Trennung der Variablen wird besonders auf die Theorie der linearen Differentialgleichungen eingegangen.

Die Gro En Fragen Mathematik

Author : Tony Crilly
ISBN : 9783827429186
Genre : Mathematics
File Size : 73. 61 MB
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Die großen Fragen behandeln grundlegende Probleme und Konzepte in Wissenschaft und Philosophie, die Forscher und Denker seit jeher umtreiben. Anspruch der ambitionierten Reihe ist es, die Antworten auf diese Fragen zu präsentieren und damit die wichtigsten Gedanken der Menschheit in einzigartigen Übersichten zu bündeln. Im vorliegenden Band Mathematik, der einen Bogen spannt vom Beginn des Zählens und den idealen Platonischen Körpern bis zur Chaostheorie und dem Fermat’schen Theorem, setzt sich Tony Crilly mit jenen 20 Fragen auseinander, die das Herz der Mathematik und unseres Verständnisses der Welt bilden.

Direkte Methoden Der Variationsrechnung

Author : Ph. Blanchard
ISBN : 9783709122600
Genre : Science
File Size : 29. 87 MB
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Einf Hrung In Die Potentialtheorie

Author : L. L. Helms
ISBN : 9783110822991
Genre : Mathematics
File Size : 40. 82 MB
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