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One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fun…
On the problem of Plateau
by Radó, Tibor
fromErgebnisse der mathematik und ihrer grenzgebiete
0
Type: Book
![On the problem of Plateau [and] Subharmonic functions](https://covers.openlibrary.org/b/isbn/9783642991189-M.jpg?default=false)
A convex function f may be called sublinear in the following sense; if a linear function l is ::=: j at the boundary points of an interval, then l:> j in the interior of that interval also. If we replace the terms interval and linear junction by the terms domain and harmonic fun…
During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold $M$ determin…
Consider the following question: Does there exist a three-manifold M for which, given any riemannian metric on M there is an area bound for embedded minimal spheres? We answer this question negatively, and, in fact, find an open set of metrics for which this question is false. T…
