Plurisubharmonic saddles

Siegfried Momm

Annales Polonici Mathematici (1996)

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

Abstract

top
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

top

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

top
  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). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.