Plurisubharmonic saddles

Siegfried Momm

Annales Polonici Mathematici (1996)

  • Volume: 63, Issue: 3, page 235-245
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Siegfried Momm. "Plurisubharmonic saddles." Annales Polonici Mathematici 63.3 (1996): 235-245. <http://eudml.org/doc/262641>.

@article{SiegfriedMomm1996,
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.},
author = {Siegfried Momm},
journal = {Annales Polonici Mathematici},
keywords = {extremal plurisubharmonic functions; uniqueness theorem; convex sets; subharmonic saddle; subharmonic function; plurisubharmonic saddles; angular derivatives of conformal mappings},
language = {eng},
number = {3},
pages = {235-245},
title = {Plurisubharmonic saddles},
url = {http://eudml.org/doc/262641},
volume = {63},
year = {1996},
}

TY - JOUR
AU - Siegfried Momm
TI - Plurisubharmonic saddles
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 3
SP - 235
EP - 245
AB - 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.
LA - eng
KW - extremal plurisubharmonic functions; uniqueness theorem; convex sets; subharmonic saddle; subharmonic function; plurisubharmonic saddles; angular derivatives of conformal mappings
UR - http://eudml.org/doc/262641
ER -

References

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  1. [1] C. O. Kiselman, The partial Legendre transform for plurisubharmonic functions, Invent. Math. 49 (1978), 137-148. Zbl0378.32010
  2. [2] M. Klimek, Pluripotential Theory, Oxford Univ. Press, 1991. 
  3. [3] 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. Zbl0723.45005
  4. [4] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474. Zbl0492.32025
  5. [5] S. Momm, Convex univalent functions and continuous linear right inverses, J. Funct. Anal. 103 (1992), 85-103. Zbl0771.46016
  6. [6] S. Momm, The boundary behavior of extremal plurisubharmonic functions, Acta Math. 172 (1994), 51-75. Zbl0802.32024
  7. [7] S. Momm, Extremal plurisubharmonic functions associated to convex pluricomplex Green functions with pole at infinity, J. Reine Angew. Math., to appear. Zbl0848.31008
  8. [8] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, 1993. Zbl0798.52001
  9. [9] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959. Zbl0087.28401
  10. [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). 

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