On the Problem of Plateau / Subharmonic Functions (Ergebnisse der Mathematik und Ihrer Grenzgebiete) - Couverture rigide

Rado, T.

Couverture rigide

ISBN 10 : 3540054790 ISBN 13 : 9783540054795

Editeur : Springer, 1971

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 1971
• Langue: anglais
• ISBN 10: 3540054790
• ISBN 13: 9783540054795
• Reliure: Relié
• Nombre de pages: 190
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne