Existence and regularity of minimal surfaces on Riemannian manifolds. (English) Zbl 0462.58003

Pitts, Jon T.

Mathematical Notes, 27. Princeton, New Jersey: Princeton University Press; University of Tokyo Press. VII, 329 p. $ 16.00 (1981).

MSC:

58-02	Research exposition (monographs, survey articles) pertaining to global analysis
58E12	Variational problems concerning minimal surfaces (problems in two independent variables)
53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
58E15	Variational problems concerning extremal problems in several variables; Yang-Mills functionals
53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
58E10	Variational problems in applications to the theory of geodesics (problems in one independent variable)
49Q05	Minimal surfaces and optimization
58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
49Q15	Geometric measure and integration theory, integral and normal currents in optimization
49Q20	Variational problems in a geometric measure-theoretic setting

Keywords:

existence and regularity of minimal surfaces on Riemannian manifolds; geodesics; minimal surfaces; second variation estimates of R. Schoen and L. Simon; locally uniquely mass minimizing k dimensional integral currents; varifold; spaces of surfaces; i-th homotopy group of the space of j-dimensional integral cycles on a k+1 dimensional Riemannian manifold; stable hypersurfaces