Differential and Riemannian geometry

This book represents the first synthesis of the considerable body of new research into positive definite matrices.

Differential geometry is the study of the curvature and calculus of curves and surfaces.

The main subject of this book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in di?

This volume arose from a semester at CIRM-Luminy on "e;Thermodynamic Formalism: Applications to Probability, Geometry and Fractals"e; which brought together leading experts in the area to discuss topical problems and recent progress.

This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms.

This volume features selected papers from The Fifteenth International Conference on Order Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz, Russia, on 15 - 20th July 2019.

This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira.

Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.

An exposition of the theory of curves over a finite field, and connections to the Riemann Hypothesis for function fields.

It isn't that they can't see the solution.

This textbook offers a concise introduction to symplectic and contact geometry, with a focus on the relationships between these subjects and other topics such as Lie theory and classical mechanics.

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015.

The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics.

This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis.

This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis.

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines.

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From Bäcklund to Darboux: a comprehensive journey through the transformation theory of constrained Willmore surfaces, with applications to constant mean curvature surfaces.

The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators.

The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations.