Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.

Martingales (Mathematics) --- Stochastic processes. --- Probabilities. --- Martingales (Mathematics). --- Stochastic processes --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Random processes --- Probabilities --- Abraham Robinson. --- Absolute value. --- Addition. --- Algebra of random variables. --- Almost surely. --- Axiom. --- Axiomatic system. --- Borel set. --- Bounded function. --- Cantor's diagonal argument. --- Cardinality. --- Cartesian product. --- Central limit theorem. --- Chebyshev's inequality. --- Compact space. --- Contradiction. --- Convergence of random variables. --- Corollary. --- Correlation coefficient. --- Counterexample. --- Dimension (vector space). --- Dimension. --- Division by zero. --- Elementary function. --- Estimation. --- Existential quantification. --- Family of sets. --- Finite set. --- Hyperplane. --- Idealization. --- Independence (probability theory). --- Indicator function. --- Infinitesimal. --- Internal set theory. --- Joint probability distribution. --- Law of large numbers. --- Linear function. --- Martingale (probability theory). --- Mathematical induction. --- Mathematician. --- Mathematics. --- Measure (mathematics). --- N0. --- Natural number. --- Non-standard analysis. --- Norm (mathematics). --- Orthogonal complement. --- Parameter. --- Path space. --- Predictable process. --- Probability distribution. --- Probability measure. --- Probability space. --- Probability theory. --- Probability. --- Product topology. --- Projection (linear algebra). --- Quadratic variation. --- Random variable. --- Real number. --- Requirement. --- Scientific notation. --- Sequence. --- Set (mathematics). --- Significant figures. --- Special case. --- Standard deviation. --- Statistical mechanics. --- Stochastic process. --- Subalgebra. --- Subset. --- Summation. --- Theorem. --- Theory. --- Total variation. --- Transfer principle. --- Transfinite number. --- Trigonometric functions. --- Upper and lower bounds. --- Variable (mathematics). --- Variance. --- Vector space. --- W0. --- Wiener process. --- Without loss of generality.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and recent advances toward general structure theorems concerning the existence of multiple solutions are explored in full detail.The book focuses on the author's derivation of the Morse-inequalities and in particular the mountain-pass-lemma of Morse-Tompkins and Shiffman for minimal surfaces and the proof of the existence of large (unstable) H-surfaces (Rellich's conjecture) due to Brezis-Coron, Steffen, and the author. Many related results are covered as well. More than the geometric aspects of Plateau's problem (which have been exhaustively covered elsewhere), the author stresses the analytic side. The emphasis lies on the variational method.Originally published in 1989.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Calculus of variations. --- Global analysis (Mathematics). --- Minimal surfaces. --- Plateau's problem. --- Global analysis (Mathematics) --- MATHEMATICS / Geometry / Differential. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Minimal surface problem --- Plateau problem --- Problem of Plateau --- Minimal surfaces --- Surfaces, Minimal --- Banach space. --- Bernhard Riemann. --- Big O notation. --- Boundary value problem. --- Branch point. --- C0. --- Closed geodesic. --- Compact space. --- Complex analysis. --- Complex number. --- Conformal map. --- Conjecture. --- Contradiction. --- Convex curve. --- Convex set. --- Differentiable function. --- Direct method in the calculus of variations. --- Dirichlet integral. --- Dirichlet problem. --- Embedding. --- Estimation. --- Euler–Lagrange equation. --- Existential quantification. --- Geometric measure theory. --- Global analysis. --- Jordan curve theorem. --- Linear differential equation. --- Mathematical analysis. --- Mathematical problem. --- Mathematician. --- Maximum principle. --- Mean curvature. --- Metric space. --- Minimal surface. --- Modulus of continuity. --- Morse theory. --- Nonparametric statistics. --- Normal (geometry). --- Parallel projection. --- Parameter space. --- Parametrization. --- Partial differential equation. --- Quadratic growth. --- Quantity. --- Riemann mapping theorem. --- Second derivative. --- Sign (mathematics). --- Special case. --- Surface area. --- Tangent space. --- Theorem. --- Total curvature. --- Uniform convergence. --- Variational method (quantum mechanics). --- Variational principle. --- W0. --- Weak solution.