Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in… (More)

1. Summary of results. The following is known: let 5 be a minimal surface defined by z=f(x, y) over the region D:x2+y2<R2, and let p be the point of S over the origin. Let W= (1+fl+fl)112 at p. Then… (More)

Given a domain D in euclidean space or on a Riemannian manifold, one naturally associates with it such fundamental geometric quantities as its volume, the measure of its boundary, various curvature… (More)

O ne of the oldest problems to have been solved using the calculus of variations was to find the equation for the shape formed by a hanging chain or flexible cord. Most often it is said that Galileo… (More)

In a talk at the 1954 International Congress,2 the author outlined an existence proof for a surface of the form z=f(x, y) which covers every point of the x, y-plane exactly once, and which is… (More)

This paper contains results of a somewhat varied nature, all obtained from a detailed examination of a special class of surfaces. These results include a method for the isometric embedding of Riemann… (More)

We prove a “general shrinking lemma” that resembles the Schwarz– Pick–Ahlfors Lemma and its many generalizations, but differs in applying to maps of a finite disk into a disk, rather than requiring… (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in… (More)

868 NOTICES OF THE AMS VOLUME 46, NUMBER 8 I n his pivotal 1916 paper [P], Georg Pick begins somewhat provocatively with the phrase, “The so-called Schwarz Lemma says...”, followed by a reference to… (More)