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.

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Editorial
Springer
Año de publicación
1971
Idioma
Inglés
ISBN 10 
3540054790
ISBN 13 
9783540054795
Encuadernación
Tapa dura
Número de páginas
190
Contacto del fabricante
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Darmstadt
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Alemania

Otras ediciones populares con el mismo título

9783642983078: On the Problem of Plateau: 2 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 2)

Edición Destacada

ISBN 10:  3642983073 ISBN 13:  9783642983078
Editorial: Springer, 1933
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