On the Problem of Plateau / Subharmonic Functions

T. Rado

ISBN 10: 3540054790 / ISBN 13: 9783540054795

Published by Springer, Springer Vieweg, 1971

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783540054795

Bibliographic Details

• Title: On the Problem of Plateau / Subharmonic Functions
• Publisher: Springer, Springer Vieweg
• Publication Date: 1971
• Language: English
• ISBN 10: 3540054790
• ISBN 13: 9783540054795
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 11D millimeters 229 millimeters width by 152 millimeters height by 11 millimeters depth
• Weight: 282 grams

About this title

Synopsis

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.