Book Titles
Surveys in Differential Geometry, Vol. IX
Surveys in Differential
Geometry, Vol. IX: Eigenvalues of Laplacians and Other Geometric Operators
ISBN: 978-1-57146-180-3
Year Published: 2010 (original hardcover publication in 2004)
Pages: 476 pages
Binding: Softcover
List Price: $39.00
Description:
This volume is a collection of surveys of diverse topics in geometry
related to the eigenvalues of the Laplacian and other geometric operators.
A good understanding of the spectral properties of differential operators
has deep consequences in geometry, physics, number theory, probability
theory, etc. Analytic methods have penetrated also into discrete mathematics,
where the study of the spectral properties of difference operators leads
to a deeper understanding of the combinatorial question on graphs. The
present collection represents a substantial part of the subject, and it
will be beneficial to geometers and experts from the adjacent area.
Contents:
Anomalous diffusion and stability of Harnack inequalities M. T. Barlow
From isoperimetric inequalities to heat kernels via symmetrisation G. Besson
Discrete isoperimetric inequalities F. Chung
An excursion into geometric analysis T. H. Colding and W. P. Minicozzi II
Eigenvalues of elliptic operators and geometric applications A. Grigor'yan, Y. Netrusov, and S.-T. Yau
Spectral gap, logarithmic Sobolev constant, and geometric bounds M. Ledoux
Discrete analytic functions: An exposition L. Lovász
Confromal properties in classical minimal surface theory W. H. Meeks III and J. Pérez
Analysis of the cut locus via the heat kernel R. Neel and D. Stroock
Analysis on Riemannian co-compact covers L. Saloff-Coste
Functoriality and small eigenvalues of Laplacian on Riemann survaces F. Shahidi
The inverse spectral problem S. Zelditch
Editors:
Alexander Grigor'yan, Imperial College of Science
and Technology, London, England S.-T. Yau, Harvard University, Cambridge, MA
Surveys in Differential Geometry, Vol. IX
