Download Full eBooks in PDF
The Heat Kernel Weighted Hodge Laplacian On Noncompact Manifolds Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of The Heat Kernel Weighted Hodge Laplacian On Noncompact Manifolds book. This book definitely worth reading, it is an incredibly well-written.
Author : Edward Lee Bueler
Publisher : Unknown
Page : 152 pages
File Size : 55,7 Mb
Release : 1997
Category : Electronic
ISBN : CORNELL:31924079838987
Author : Alexander Grigor'yan
Publisher : American Mathematical Soc.
Page : 504 pages
File Size : 42,6 Mb
Release : 2009
Category : Gaussian processes
ISBN : 9780821893937
The heat kernel has long been an essential tool in both classical and modern mathematics but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation. The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety of settings. The exposition starts with an elementary introduction to Riemannian geometry, proceeds with a thorough study of the spectral-theoretic, Markovian, and smoothness properties of the Laplace and heat equations on Riemannian manifolds, and concludes with Gaussian estimates of heat kernels. Grigor'yan has written this book with the student in mind, in particular by including over 400 exercises. The text will serve as a bridge between basic results and current research.Titles in this series are co-published with International Press, Cambridge, MA, USA.
Author : Yoshiaki Maeda,Peter Michor,Takushiro Ochiai,Akira Yoshioka
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 48,9 Mb
Release : 2007-04-22
Category : Mathematics
ISBN : 9780817645304
* Invited articles in differential geometry and mathematical physics in honor of Hideki Omori * Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry * Will appeal to graduate students in mathematics and quantum mechanics; also a reference
Author : Analysis on Infinit Ams Special Session,Hui-Hsiung Kuo,Ambar Sengupta
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 44,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821832028
This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross' former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross' work and permeate diverse fields. Topics of this title include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.
Author : Henry Han,Tie Wei,Wenbin Liu,Fei Han
Publisher : Springer Nature
Page : 295 pages
File Size : 42,7 Mb
Release : 2020-09-28
Category : Computers
ISBN : 9789811587603
This book constitutes selected papers of the Third International Conference on Data Science, Medicine and Bioinformatics, IDMB 2019, held in Nanning, China, in June 2019. The 19 full papers and 1 short paper were carefully reviewed and selected from 93 submissions. The papers are organized according to the following topical sections: business data science: fintech, management, and analytics.- health and biological data science.- novel data science theory and applications.
Author : Giovanni Catino,Paolo Mastrolia
Publisher : Springer Nature
Page : 247 pages
File Size : 40,8 Mb
Release : 2020-10-23
Category : Mathematics
ISBN : 9783030571856
This book focuses on a selection of special topics, with emphasis on past and present research of the authors on “canonical” Riemannian metrics on smooth manifolds. On the backdrop of the fundamental contributions given by many experts in the field, the volume offers a self-contained view of the wide class of “Curvature Conditions” and “Critical Metrics” of suitable Riemannian functionals. The authors describe the classical examples and the relevant generalizations. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
Author : Stephen Spratlin Bullock
Publisher : Unknown
Page : 334 pages
File Size : 52,9 Mb
Release : 2000
Category : Electronic
ISBN : CORNELL:31924088873025
Author : Shilong Kuang
Publisher : Unknown
Page : 172 pages
File Size : 54,6 Mb
Release : 2009
Category : Geometry, Differential
ISBN : UCR:31210022939753
Author : Steven Rosenberg
Publisher : Cambridge University Press
Page : 188 pages
File Size : 53,8 Mb
Release : 1997-01-09
Category : Mathematics
ISBN : 0521463009
This text on analysis on Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The author develops the Atiyah-Singer index theorem and its applications (without complete proofs) via the heat equation method. Rosenberg also treats zeta functions for Laplacians and analytic torsion, and lays out the recently uncovered relation between index theory and analytic torsion. The text is aimed at students who have had a first course in differentiable manifolds, and the author develops the Riemannian geometry used from the beginning. There are over 100 exercises with hints.
Author : Anonim
Publisher : Unknown
Page : 362 pages
File Size : 54,6 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015072602108
Author : Jay Jorgenson,Lynne Walling
Publisher : American Mathematical Soc.
Page : 412 pages
File Size : 48,7 Mb
Release : 2006
Category : Mathematics
ISBN : 0821857304
The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.
Author : Pierre Albin,Frédéric Rochon,David Sher
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 48,8 Mb
Release : 2021-06-21
Category : Education
ISBN : 9781470444228
Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.
Author : Anonim
Publisher : Unknown
Page : 1208 pages
File Size : 52,9 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015078588608
Author : Anonim
Publisher : Unknown
Page : 794 pages
File Size : 52,5 Mb
Release : 2005
Category : Dissertations, Academic
ISBN : STANFORD:36105121649169
Author : Jean-Michel Bismut
Publisher : Princeton University Press
Page : 343 pages
File Size : 46,7 Mb
Release : 2011-08-08
Category : Mathematics
ISBN : 9781400840571
This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof.