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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.2 Temuco  2010 

CUBO A Mathematical Journal Vol.12, N° 02, (235–259). June 2010


On Semisubmedian Functions and Weak Plurisubharmonicity

Chia-chi Tung1

Dept. of Mathematics and Statistics, Minnesota State University, Mankato, Mankato, MN 56001, USA email:


In this note subharmonic and plurisubharmonic functions on a complex space are studied intrinsically. For applications subharmonicity is characterized more effectually in terms of properties that need be verified only locally off a thin analytic subset; these include the submean-value inequalities, the spherical (respectively, solid) monotonicity, near as well as weak subharmonicity. Several results of Gunning [9, K and L] are extendable via regularity to complex spaces. In particular, plurisubharmonicity amounts (on a normal space) essentially to regularized weak plurisubharmonicity, and similarly for subharmonicity (on a general space). A generalized Hartogs' lemma and constancy criteria for certain matrix-valued mappings are given.

Key words and phrases: Subharmonicity, seminear subharmonicity, Jensen function, weak subharmonicity, weak plurisubharmonicity


En esta nota son estudiadas intrínsicamente las funciones subarmonicas y plurisubarmonicas sobre un espacio complejo. Para aplicaciones, subarmonicidad es caracterizada mas eficientemente en términos de propiedades que necesitan ser verificadas solamente localmente en un subconjunto analítico delgado; estas aplicaciones incluyen la desigualdad del valor-submedio, la monotonicidad esférica (respectivamente, sólida), bien como subarmonicidad debil. Varios resultados de Gunning [9, K and L] son extendibles vía regularidad a espacios complejos. En particular, plurisubarmonicidad (sobre un espacio normal) importa esencialmente para plurisubarmonicidad débil regularizada y similarmente para subarmoniciada (sobre un espacio general). Son dados un lema de Hartogs generalizado y un criterio de constancia para ciertas aplicaciones matriz-valuada.

2000 Math. Subj. Class.: Primary: 31C05; Secondary: 31C10, 32C15


1Supports by the ”Globale Methoden in der komplexen Geometrie” Grant of the German research society DFG and the Faculty Improvement Grant of Minnesota State University, Mankato, are gratefully acknowledged.


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Received: January 2009.

Revised: May 2009.

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