Books in the Lecture Notes in Mathematics series

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement.

Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This CIME course focused on complex Monge-Ampere equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics.

The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields.

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors' 2007 Springer monograph "Random Fields and Geometry." While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level.

The main ideas are illustrated in the context of three different physical problems:(i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous.

This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images.

This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths.

Starting with convex functions on the line, this title leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational principles and perturbed optimization.

The book deals with linear time-invariant delay-differential equations with commensurated point delays in a control-theoretic context. The aim is to show that with a suitable algebraic setting a behavioral theory for dynamical systems described by such equations can be developed.

The Nonlinear Optimization problem of main concern here is the problem n of determining a vector of decision variables x ? R that minimizes (ma- n mizes) an objective function f(*): R ? R , usually described by a set of equality and - n n m equality constraints: F = {x ? R : h(x)=0,h(*): R ? 0, n p g(*): R ?

The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function.

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.

The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper "Diophantine approximation onabelian varieties", Ann. Eachchapter is based on an instructional lecture given by itsauthor ata special conference for graduate students, on thetopic of Faltings' paper.

In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes.

This book is an introduction to main methods and principalresults in the theory of Co(remark: o is upperindex!!)-small perturbations of dynamical systems.

This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions.

Lectures Given at the Inter-University Center of Postgraduate Studies, Dubrovnik, Yugoslavia, November 3-17, 1985

Zeta functions have been a powerful tool in mathematics over the last two centuries. The book examines many important examples of zeta functions, providing an important database of explicit examples and methods for calculation.

The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincare inequalities, and spectral synthesis theorems.

Lectures given at the Banach Center and C.I.M.E. Joint Summer School held in Bedlewo, PolandSeptember 4-9, 2006