Details

Autor(en) / Beteiligte

• Radó, Tibor

Titel

On the Problem of Plateau/Subharmonic Functions [Elektronische Ressource]

Ist Teil von

• Ergebnisse der Mathematik und Ihrer Grenƶgebiete, Herausgegeben Von Der Schriftleitung des „Ƶentralblatt für Mathematik“ Fünfter Band : 2

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

1971

Link zum Volltext

• Volltext

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• 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 generalization, formulated and developed by F. RIEsz, immediately attracted 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-distribution is subharmonic. In differential geometry, surfaces of negative curvature and minimal surfaces can be characterized in terms of subharmonic 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 inexhaustible source of new theorems on subharmonic functions, either by analogy or by direct implication