Geometry V
Subtitle: Minimal Surfaces (Encyclopaedia of Mathematical Sciences)
Contributors: H. Fujimoto (Contributor); S. Hildebrandt (Contributor); D. Hoffmann (Contributor); H. Karcher (Contributor); L. Simon (Contributor); Robert Osserman (Editor)
Edition: 1 edition
Publisher: Springer
Published: November 13, 1997
Language: eng
Format: Hardcover
Number of pages: 272
ISBN-13: 9783540605232
Subjects: Complex analysis; Differential & Riemannian geometry; Differential Geometry; Mathematics; Science/Mathematics; Geometry - Differential; Applied; Mathematical Analysis; Mathematics / Geometry / Differential; Nevanlina theory; calculus of variations; minimal surfaces; partial differential equations
First sentence: We will survey what is known about minimal surfaces S C R3, which are complete, embedded, and have finite total curvature: S K dA &lt;.
Description: Osserman (Ed.) Geometry V Minimal Surfaces The theory of minimal surfaces has expanded in many directions over the past decade or two. This volume gathers in one place an overview of some of the most exciting developments, presented by five of the leading contributors to those developments. Hirotaka Fujimoto, who obtained the definitive results on the Gauss map of minimal surfaces, reports on Nevanlinna Theory and Minimal Surfaces. Stefan Hildebrandt provides an up-to-date account of the Plateau problem and related boundary-value problems. David Hoffman and Hermann Karcher describe the wealth of results on embedded minimal surfaces from the past decade, starting with Costa's surface and the subsequent Hoffman-Meeks examples. Finally, Leon Simon covers the PDE aspect of minimal surfaces, with a survey of known results both in the classical case of surfaces and in the higher dimensional case. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics.