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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
On the Problem of Plateau / Subharmonic Functions

On the Problem of Plateau / Subharmonic Functions

Rado, T.

Paperback

Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 1. Folge, Book 2

General Mathematics

ISBN10: 3540054790
ISBN13: 9783540054795
Publisher: Springer Nature
Published: Jan 4 1971
Pages: 109
Weight: 0.57
Height: 0.40 Width: 6.00 Depth: 9.00
Language: English
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.

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