Plurisubharmonic saddles

Siegfried Momm

ArticleOriginal scientific text

Title

Plurisubharmonic saddles

Authors ¹

Affiliations

Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstr. 1, 40225 Düsseldorf, Germany

Abstract

A certain linear growth of the pluricomplex Green function of a bounded convex domain of

ℂ^{N}

at a given boundary point is related to the existence of a certain plurisubharmonic function called a "plurisubharmonic saddle". In view of classical results on the existence of angular derivatives of conformal mappings, for the case of a single complex variable, this allows us to deduce a criterion for the existence of subharmonic saddles.

Keywords

ENG

extremal plurisubharmonic functions, uniqueness theorem, convex sets

C. O. Kiselman, The partial Legendre transform for plurisubharmonic functions, Invent. Math. 49 (1978), 137-148.
M. Klimek, Pluripotential Theory, Oxford Univ. Press, 1991.
A. S. Krivosheev, A criterion for the solvability of nonhomogeneous convolution equations in convex domains of $ℂ^{N}$ , Math. USSR-Izv. 36 (1991), 497-517.
L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474.
S. Momm, Convex univalent functions and continuous linear right inverses, J. Funct. Anal. 103 (1992), 85-103.
S. Momm, The boundary behavior of extremal plurisubharmonic functions, Acta Math. 172 (1994), 51-75.
S. Momm, Extremal plurisubharmonic functions associated to convex pluricomplex Green functions with pole at infinity, J. Reine Angew. Math., to appear.
R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, 1993.
M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959.
V. P. Zakharyuta, Extremal plurisubharmonic functions, Hilbert scales and isomorphisms of spaces of analytic functions, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen., part I, 19 (1974), 133-157, part II, 21 (1974), 65-83 (in Russian).

Title

Plurisubharmonic saddles

Affiliations

Abstract

Keywords

Bibliography