A certain linear growth of the pluricomplex Green function of a bounded convex domain of 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.
@article{bwmeta1.element.bwnjournal-article-apmv63z3p235bwm, author = {Siegfried Momm}, title = {Plurisubharmonic saddles}, journal = {Annales Polonici Mathematici}, volume = {63}, year = {1996}, pages = {235-245}, zbl = {0867.31001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv63z3p235bwm} }
Siegfried Momm. Plurisubharmonic saddles. Annales Polonici Mathematici, Tome 63 (1996) pp. 235-245. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z3p235bwm/
[000] [1] C. O. Kiselman, The partial Legendre transform for plurisubharmonic functions, Invent. Math. 49 (1978), 137-148. | Zbl 0378.32010
[001] [2] M. Klimek, Pluripotential Theory, Oxford Univ. Press, 1991.
[002] [3] A. S. Krivosheev, A criterion for the solvability of nonhomogeneous convolution equations in convex domains of , Math. USSR-Izv. 36 (1991), 497-517. | Zbl 0723.45005
[003] [4] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474. | Zbl 0492.32025
[004] [5] S. Momm, Convex univalent functions and continuous linear right inverses, J. Funct. Anal. 103 (1992), 85-103. | Zbl 0771.46016
[005] [6] S. Momm, The boundary behavior of extremal plurisubharmonic functions, Acta Math. 172 (1994), 51-75. | Zbl 0802.32024
[006] [7] S. Momm, Extremal plurisubharmonic functions associated to convex pluricomplex Green functions with pole at infinity, J. Reine Angew. Math., to appear. | Zbl 0848.31008
[007] [8] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, 1993. | Zbl 0798.52001
[008] [9] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959. | Zbl 0087.28401
[009] [10] 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).