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 : 22. 85 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 : 48. 59 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 : 75. 5 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 : 83. 41 MB
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Contains the material taught during a series of lectures given at Zhejiang University in Hangzhou between 2010 and 2012.

Quantitative Wirtschaftsforschung

Author : Ernst Helmstädter
ISBN : STANFORD:36105035677959
Genre : Economics
File Size : 35. 99 MB
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