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On the Problem of Plateau / Subharmonic Functions (Ergebnisse der Mathematik und Ihrer Grenzgebiete): 2 (Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge, 2) - Tapa dura

Rado, T.

 
9783540054795: On the Problem of Plateau / Subharmonic Functions (Ergebnisse der Mathematik und Ihrer Grenzgebiete): 2 (Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge, 2)
Tapa dura
ISBN 10: 3540054790 ISBN 13: 9783540054795
Editorial: Springer, 1971

Sinopsis

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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Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
1971
Idioma
Inglés
ISBN 10 
3540054790
ISBN 13 
9783540054795
Encuadernación
Tapa dura
Número de páginas
190
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