Differential geometry is a mathematical discipline that uses the techniques of differential calculus and integral calculus, as well as linear algebra and multilinear algebra, to study problems in geometry.
This volume contains extended abstracts outlining selected talks and other selected presentations given by participants of the workshop "e;Positivity and Valuations"e;, held at the Centre de Recerca Matematica (CRM) in Barcelona from February 22nd to 26th, 2016.
Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations.
Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility.
For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators.
The characterization of combinatorial or geometric structures in terms of their groups of automorphisms has attracted considerable interest in the last decades and is now commonly viewed as a natural generalization of Felix Klein's Erlangen program(1872).
Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra.
This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members.
The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date.
Regularity Techniques for Elliptic PDEs and the Fractional Laplacian presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian.
Appliies variational methods and critical point theory on infinite dimenstional manifolds to some problems in Lorentzian geometry which have a variational nature, such as existence and multiplicity results on geodesics and relations between such geodesics and the topology of the manifold.
Twistor theory is the remarkable mathematical framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory.
This book presents new and original results on the deformations of apparent contours of surfaces in Euclidean 3-space and the discriminants of plane-to-plane map-germs.
This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the "e;Higher homotopical structures"e; programme.
Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups).
Geometry of Derivation with Applications is the fifth work in a longstanding series of books on combinatorial geometry (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes, and Combinatorics of Spreads and Parallelisms).
This book provides a critical edition, translation, and study of the version of Euclid's treatise made by Thabit ibn Qurra, which is the earliest Arabic version that we have in its entirety.
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact.
In diesem Lehrbuch stellen die Autoren einen axiomatischen Zugang zur ebenen Geometrie dar, der im Vergleich zu den Hilbertaxiomen und anderen oft gewählten Zugängen strukturelle und didaktische Vorteile bietet.
This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe.
This text offers a selection of papers on singularity theory presented at the Sixth Workshop on Real and Complex Singularities held at ICMC-USP, Brazil.
An unparalleled illustrated history of spherical trigonometry from antiquity to todayHeavenly Mathematics traces the rich history of spherical trigonometry, revealing how the cultures of classical Greece, medieval Islam, and the modern West used this forgotten art to chart the heavens and the Earth.
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.
El Algebra lineal y su interpretación geométrica se ha constituido en un bloque de conocimiento común e indispensable tanto en las licenciaturas de Ciencias como en las Ingenierías técnicas y superiores.
This thesis deals with specific featuresof the theory of holomorphic dynamics in dimension 2 and then sets out to studyanalogous questions in higher dimensions, e.
Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics.
Foreword by S S Chern In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds.
A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
Differential geometry is a mathematical discipline that uses the techniques of differential calculus and integral calculus, as well as linear algebra and multilinear algebra, to study problems in geometry.
