02830nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184100003100220245008500251260008200336300003400418336002600452337002600478338003600504347002400540490003900564506006600603520146500669650004502134650004802179650004002227650002502267650006602292856003202358856006602390186-150225CH-001817-320150225234500.0a fot ||| 0|cr nn mmmmamaa150225e20150218sz fot ||| 0|eng d a978303719651970a10.4171/1512doi ach0018173 7aPBK2bicssc a58-xxa35-xxa47-xxa49-xx2msc1 aLablée, Olivier,eauthor.10aSpectral Theory in Riemannian Geometryh[electronic resource] /cOlivier Lablée3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (197 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSpectral theory is a diverse area of mathematics that derives its motivations, goals and impetus from several sources. In particular, the spectral theory of the Laplacian on a compact Riemannian manifold is a central object in differential geometry. From a physical point a view, the Laplacian on a compact Riemannian manifold is a fundamental linear operator which describes numerous propagation phenomena: heat propagation, wave propagation, quantum dynamics, etc. Moreover, the spectrum of the Laplacian contains vast information about the geometry of the manifold.
This book gives a self-containded introduction to spectral geometry on compact Riemannian manifolds. Starting with an overview of spectral theory on Hilbert spaces, the book proceeds to a description of the basic notions in Riemannian geometry. Then its makes its way to topics of main interests in spectral geometry. The topics presented include direct and inverse problems. Direct problems are concerned with computing or finding properties on the eigenvalues while the main issue in inverse problems is “knowing the spectrum of the Laplacian, can we determine the geometry of the manifold?”
Addressed to students or young researchers, the present book is a first introduction in spectral theory applied to geometry. For readers interested in pursuing the subject further, this book will provide a basis for understanding principles, concepts and developments of spectral geometry.07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc07aPartial differential equations2msc07aOperator theory2msc07aCalculus of variations and optimal control; optimization2msc40uhttps://doi.org/10.4171/151423cover imageuhttps://www.ems-ph.org/img/books/lablee_mini.jpg