The Heat Kernel Weighted Hodge Laplacian On Noncompact Manifolds
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Heat Kernel and Analysis on Manifolds
Author | : Alexander Grigoryan |
Publisher | : American Mathematical Soc. |
Total Pages | : 504 |
Release | : 2009 |
Genre | : Education |
ISBN | : 0821893939 |
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.
A Perspective on Canonical Riemannian Metrics
Author | : Giovanni Catino |
Publisher | : Springer Nature |
Total Pages | : 247 |
Release | : 2020-10-23 |
Genre | : Mathematics |
ISBN | : 3030571858 |
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.
From Geometry to Quantum Mechanics
Author | : Yoshiaki Maeda |
Publisher | : Springer Science & Business Media |
Total Pages | : 326 |
Release | : 2007-04-22 |
Genre | : Mathematics |
ISBN | : 0817645306 |
* 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
Finite and Infinite Dimensional Analysis in Honor of Leonard Gross
Author | : Hui-Hsiung Kuo |
Publisher | : American Mathematical Soc. |
Total Pages | : 242 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821832026 |
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's 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's work and permeate diverse fields. Topics 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.
Abstracts of Papers Presented to the American Mathematical Society
Author | : American Mathematical Society |
Publisher | : |
Total Pages | : 658 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : |
The Ubiquitous Heat Kernel
Author | : Jay Jorgenson |
Publisher | : American Mathematical Soc. |
Total Pages | : 410 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821836986 |
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.
Recent Advances in Data Science
Author | : Henry Han |
Publisher | : Springer Nature |
Total Pages | : 295 |
Release | : 2020-09-28 |
Genre | : Computers |
ISBN | : 9811587604 |
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.