The three-volume treatise consists of the volumes Minimal Surfaces (GL 339), Regularity of Minimal Surfaces (GL 340), and Glolbal Theory of Minimal Surfaces (GL 341) that replace the monograph Minimal Surfaces I, II, published as volumes 295 and 296 of the Grundlehren der mathematischen Wissenschaft series.
Ther first volume covers the classical theory as well as existence results concerning boundary value problems for minimal surfaces, in particular results for Plateau's problem.
The second volume deals with basic regularity results for minimal...
The three-volume treatise consists of the volumes Minimal Surfaces (GL 339), Regularity of Minimal Surfaces (GL 340), and Glolbal ...
J. Neveu, 1962 in Zentralblatt fur Mathematik, 92.Band Heft 2, p. 343: "Ce livre ecrit par l'un des plus eminents specialistes en la matiere, est un expose tres detaille de la theorie des processus de Markov definis sur un espace denombrable d'etats et homogenes dans le temps (chaines stationnaires de Markov)."
N.Jain, 2008 in Selected Works of Kai Lai Chung, edited by Farid AitSahlia (University of Florida, USA), Elton Hsu (Northwestern University, USA), & Ruth Williams (University of California-San Diego, USA), Chapter 1, p. 15: "This monograph deals with countable...
From the reviews:
J. Neveu, 1962 in Zentralblatt fur Mathematik, 92.Band Heft 2, p. 343: "Ce livre ecrit par l'un des plus eminents specialistes en...
Therandom-clustermodelwasinventedbyCees Kees]FortuinandPietKasteleyn around 1969 as a uni?cation of percolation, Ising, and Potts models, and as an extrapolation of electrical networks. Their original motivation was to harmonize the series and parallel laws satis?ed by such systems. In so doing, they initiated a study in stochastic geometry which has exhibited beautiful structure in its own right, and which has become a central tool in the pursuit of one of the oldest challenges of classical statistical mechanics, namely to model and analyse the ferromagnet and especially its phase...
Therandom-clustermodelwasinventedbyCees Kees]FortuinandPietKasteleyn around 1969 as a uni?cation of percolation, Ising, and Potts models, and as an ex...
We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the...
We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is ...
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as weIl as Hamilton Jacobi theory and the classical theory of partial differential equations of first order. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus...
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deal...
From the reviews: "...focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field...requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex...
From the reviews: "...focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distin...
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponen...
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as well as Hamilton Jacobi theory and the classical theory of partial differential equations of first ordel;. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus...
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deal...
The present book deals with some basic problems of Approximation Theory: with properties of polynomials and splines, with approximation by poly- mials, splines, linear operators. It also provides the necessary material ab out different function spaces. In some sense, this is a modern version of the corre- sponding parts of the book of one of us (Lorentz A-1966]). We have tried to give a complete exposition of the main, basic theorems of the theory, without going into too much detail, treating the most general cases or discussing very special problems. There are essential limitations: this is...
The present book deals with some basic problems of Approximation Theory: with properties of polynomials and splines, with approximation by poly- mials...
Die MATHIEuschen Funktionen und die Spharoidfunktionen treten 2 unter anderem bei der Separation der SchwingungsgleichungL1u+ku=o in elliptischen Zylinderkoordinaten bzw. in rotationselliptischen Koor dinaten auf und stellen, von dieser Seite aus betrachtet, Verallgemei nerungen der trigonometrischen Funktionen, Zylinderfunktionen, Kugel funktionen und konfluenten hypergeometrischen Funktionen dar. Ist es schon vom mathematischen Standpunkt aus interessant, die MATHIEU schen Funktionen und die Spharoidfunktionen als Interpolation zwischen ihren wohlvertrauten Spezialfallen bzw. Ausartungen zu...
Die MATHIEuschen Funktionen und die Spharoidfunktionen treten 2 unter anderem bei der Separation der SchwingungsgleichungL1u+ku=o in elliptischen Zyli...
