By Jacques Gasqui,Hubert Goldschmidt
This ebook presents the 1st unified exam of the connection among Radon transforms on symmetric areas of compact variety and the infinitesimal types of 2 basic pressure difficulties in Riemannian geometry. Its fundamental concentration is the spectral stress challenge: Can the metric of a given Riemannian symmetric house of compact variety be characterised by way of the spectrum of its Laplacian? It additionally addresses a query rooted within the Blaschke challenge: Is a Riemannian metric on a projective house whose geodesics are all closed and of a similar size isometric to the canonical metric?
The authors comprehensively deal with the implications referring to Radon transforms and the infinitesimal models of those difficulties. Their major outcome signifies that such a lot Grassmannians are spectrally inflexible to the 1st order. this can be relatively very important, for there are nonetheless few isospectrality effects for definitely curved areas and those are the 1st such effects for symmetric areas of compact form of rank >1. The authors take advantage of the speculation of overdetermined partial differential equations and harmonic research on symmetric areas to supply standards for infinitesimal stress that observe to a wide classification of spaces.
an excessive amount of easy fabric approximately Riemannian geometry, symmetric areas, and Radon transforms is incorporated in a transparent and stylish presentation that would be worthy to researchers and complex scholars in differential geometry.
By I.M. Gelfand,James Lepowsky,Mikhail M. Smirnov
By Olivier Druet,Emmanuel Hebey,Frédéric Robert
Elliptic equations of serious Sobolev progress were the objective of research for many years simply because they've got proved to be of serious significance in research, geometry, and physics. The equations studied listed below are of the well known Yamabe kind. They contain Schrödinger operators at the left hand aspect and a severe nonlinearity at the correct hand side.
an important improvement within the examine of such equations happened within the Nineteen Eighties. It was once came upon that the series splits right into a answer of the restrict equation--a finite sum of bubbles--and a relaxation that converges strongly to 0 within the Sobolev area together with sq. integrable capabilities whose gradient can be sq. integrable. This splitting is called the crucial idea for blow-up. during this e-book, the authors improve the pointwise concept for blow-up. They introduce new rules and strategies that bring about sharp pointwise estimates. those estimates have vital functions while facing sharp consistent difficulties (a case the place the strength is minimum) and compactness effects (a case the place the power is arbitrarily large). The authors conscientiously and carefully describe pointwise habit whilst the strength is arbitrary.
meant to be as self-contained as attainable, this obtainable publication will curiosity graduate scholars and researchers in quite a number mathematical fields.
By V. Lakshmibai,K. N. Raghavan
Schubert forms supply an inductive software for learning flag types. This publication is principally a close account of a very fascinating example in their incidence: particularly, when it comes to classical invariant concept. extra accurately, it's in regards to the connection among the 1st and moment primary theorems of classical invariant idea at the one hand and conventional monomial thought for Schubert forms in sure distinct flag forms at the different.
By Victor P. Snaith
By Alexander Schmitt
By Alexander Isaev
By Martin Arkowitz
By Temitope James
The identify of this booklet is a fabricated from the flavour of arithmetic. Make this e-book in your companion to unravel each one subject and discover ways to resolve questions with supervision or on your own. study the ideas of solution of questions and solution them easily.
This publication definitely fit your wishes within the pursuit of information and realizing of arithmetic. "Mathematics is your nutrients" is a robust conviction for critical scholars of arithmetic who desired to bring up the ability and power of the answer of concerns in strict arithmetic. purchase the booklet and revel in the flavour of mathematics
By Rafal Ablamowicz,Garret Sobczyk
The topic of Clifford (geometric) algebras bargains a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is gifted via six of the world's best specialists within the box; it features an introductory bankruptcy on Clifford algebras, via broad explorations in their purposes to physics, desktop technology, and differential geometry. The book is perfect for graduate scholars in arithmetic, physics, and computing device technological know-how; it really is appropriate both for beginners who have little previous wisdom of the sphere and professionals who desire to continue abreast of the most recent applications.