| On the Problem of Plateau / Subharmonic Functions Reprint of the Edition Contributor(s): Rado, T. (Author) |
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ISBN: 3540054790 ISBN-13: 9783540054795 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: January 1971 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis |
| Dewey: 517.5 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 1. Folge |
| Physical Information: 0.4" H x 6" W x 9" (0.57 lbs) 109 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 function, we obtain a statement which expresses the characteristic property of subharmonic functions of two or more variables. This ge- neralization, formulated and developed by F. RIEsz, immediately at- tracted the attention of many mathematicians, both on account of its intrinsic interest and on account of the wide range of its applications. If f (z) is an analytic function of the complex variable z = x + i y. then If (z) I is subharmonic. The potential of a negative mass-distribu- tion is subharmonic. In differential geometry, surfaces of negative curvature and minimal surfaces can be characterized in terms of sub- harmonic functions. The idea of a subharmonic function leads to significant applications and interpretations in the fields just referred to, and- conversely, every one of these fields is an apparently in- exhaustible source of new theorems on subharmonic functions, either by analogy or by direct implication. |