On the Problem of Plateau / Subharmonic Functions (Paperback) (ISBN-13: 9783540054795)

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.

Author: T. Rado
ISBN-10: 3540054790
ISBN-13: 9783540054795
Publisher: Springer
Language: English
Published: 01/04/1971
Pages: 109
Format: Paperback
Weight: 0.57lbs
Size: 9.00h x 6.00w x 0.40d