Geometric Analysis And Pdes
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Author | : Stefan Hildebrandt |
Publisher | : Springer Science & Business Media |
Total Pages | : 663 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642556272 |
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
Author | : Matthew J. Gursky |
Publisher | : Springer Science & Business Media |
Total Pages | : 296 |
Release | : 2009-06-26 |
Genre | : Mathematics |
ISBN | : 3642016731 |
This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.
Author | : Francois Treves |
Publisher | : American Mathematical Soc. |
Total Pages | : 426 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821833863 |
This volume is dedicated to Francois Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures. An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry. The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.
Author | : Valentin Lychagin |
Publisher | : MDPI |
Total Pages | : 204 |
Release | : 2021-09-03 |
Genre | : Mathematics |
ISBN | : 303651046X |
This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.
Author | : Agostino Prastaro |
Publisher | : World Scientific |
Total Pages | : 482 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 9789810214074 |
This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Author | : Joaqun Prez |
Publisher | : American Mathematical Soc. |
Total Pages | : 198 |
Release | : 2012-07-16 |
Genre | : Mathematics |
ISBN | : 0821849921 |
This volume contains research and expository articles from the courses and talks given at the RSME Lluis A. Santalo Summer School, ``Geometric Analysis'', held June 28-July 2, 2010, in Granada, Spain. The goal of the Summer School was to present some of the many advances currently taking place in the interaction between partial differential equations and differential geometry, with special emphasis on the theory of minimal surfaces. This volume includes expository articles about the current state of specific problems involving curvature and partial differential equations, with interactions to neighboring fields such as probability. An introductory, mostly self-contained course on constant mean curvature surfaces in Lie groups equipped with a left invariant metric is provided. The volume will be of interest to researchers, post-docs, and advanced PhD students in the interface between partial differential equations and differential geometry.
Author | : S. Alinhac |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2010-05-20 |
Genre | : Mathematics |
ISBN | : 1139485814 |
Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.
Author | : Matthew J. Gursky |
Publisher | : Springer |
Total Pages | : 256 |
Release | : 2009-08-29 |
Genre | : Mathematics |
ISBN | : 9783642016752 |
This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.
Author | : Giovanna Citti |
Publisher | : Birkhäuser |
Total Pages | : 178 |
Release | : 2015-04-28 |
Genre | : Mathematics |
ISBN | : 3034804083 |
This book contains an expanded version of lectures delivered by the authors at the CRM in Spring of 2009. It contains four series of lectures. The first one is an application of harmonic analysis and the Heisenberg group to understand human vision. The second and third series of lectures cover some of the main topics on linear and multilinear harmonic analysis. The last one is a clear introduction to a deep result of De Giorgi, Moser and Nash on regularity of elliptic partial differential equations in divergence form.
Author | : Stefano Pigola |
Publisher | : Springer Science & Business Media |
Total Pages | : 294 |
Release | : 2008-05-28 |
Genre | : Mathematics |
ISBN | : 3764386428 |
This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.