Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0545.49018
Giusti, Enrico
Minimal surfaces and functions of bounded variation. (English)
[B] Monographs in Mathematics, Vol. 80. Boston-Basel-Stuttgart: Birkhäuser. XII, 240 p. DM 96.00 (1984).

This book presents a theory of parametric and non-parametric minimal hypersurfaces in euclidean spaces of arbitrary dimension. The first part of the book is devoted to parametric minimal surfaces and contains 11 chapters: Functions of bounded variation and Caccioppoli Sets; Traces of BV functions; The Reduced Boundary; Regularity of the Reduced Boundary; Some Inequalities; Approximation of Minimal Sets, I and II; Regularity of Minimal Surfaces; Minimal Cones; The First and Second Variation of the Area; The Dimension of the Singular Set. Its informal contents is existence and regularity almost everywhere of solutions to the Plateau problem and the problem on the dimension of the singular set. This part presents theorems of E. De Giorgi, L. Simons, H. Federer. \par The second part of the book is devoted to non-parametric minimal surfaces and contains 6 chapters: Classical Solutions of the Minimal Surface Equation; The a priori Estimate of the Gradient; Direct Methods; Boundary Regularity; A Further Extension of the Notion of Non-Parametric Minimal Surfaces; The Bernstein Problem. \par At the end of the book there are three small addenda devoted to some variants of the De la Vallée Poussin theorem, the distance function and elliptic equations of the second order. On the whole this book is a research level monograph in which the latest results are presented; it will be a useful reference book for mathematicians working in minimal surfaces, elliptic differential equations, geometric measure theory, capillarity and plasticity.
[P.P.Zabrejko]

MSC 2000:: *49Q05 Minimal surfaces (calculus of variations)
49-02 Research monographs (calculus of variations)
26B30 Absolutely continuous functions, etc. (several real variables)
35J20 Second order elliptic equations, variational methods
35B65 Smoothness of solutions of PDE
49Q15 Geometric measure and integration theory, etc.
49Q20 Variational problems in geometric measure-theoretic setting
53A10 Minimal surfaces, surfaces with prescribed mean curvature

Keywords: parametric and non-parametric minimal hypersurfaces; Plateau problem

Cited in: Zbl 1119.49034 Zbl 1116.49021 Zbl 0957.49001 Zbl 0825.49059 Zbl 0699.49004 Zbl 0709.49024

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]