C approximations of convex, subharmonic, and plurisubharmonic functions

R. E. Greene; H. Wu

Annales scientifiques de l'École Normale Supérieure (1979)

  • Volume: 12, Issue: 1, page 47-84
  • ISSN: 0012-9593

How to cite

top

Greene, R. E., and Wu, H.. "$C^\infty $ approximations of convex, subharmonic, and plurisubharmonic functions." Annales scientifiques de l'École Normale Supérieure 12.1 (1979): 47-84. <http://eudml.org/doc/82031>.

@article{Greene1979,
author = {Greene, R. E., Wu, H.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {convex, subharmonic, plurisubharmonic functions; functions on Riemannian manifolds; smooth approximations of continuous functions; partitions of unity; smoothing by convolution},
language = {eng},
number = {1},
pages = {47-84},
publisher = {Elsevier},
title = {$C^\infty $ approximations of convex, subharmonic, and plurisubharmonic functions},
url = {http://eudml.org/doc/82031},
volume = {12},
year = {1979},
}

TY - JOUR
AU - Greene, R. E.
AU - Wu, H.
TI - $C^\infty $ approximations of convex, subharmonic, and plurisubharmonic functions
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1979
PB - Elsevier
VL - 12
IS - 1
SP - 47
EP - 84
LA - eng
KW - convex, subharmonic, plurisubharmonic functions; functions on Riemannian manifolds; smooth approximations of continuous functions; partitions of unity; smoothing by convolution
UR - http://eudml.org/doc/82031
ER -

References

top
  1. [1] L. AHLFORS and L. SARIO, Riemann Surfaces (Princeton Mathematical Series, N°. 26, Princeton University Press, Princeton, N.J. 1960). Zbl0196.33801MR22 #5729
  2. [2] M. BERGER, P. GAUDUCHON and E. MAZET, Le spectre d'une variété riemannienne (Lecture Notes in Math., No. 194, Springer-Verlag, New York, 1971). Zbl0223.53034MR43 #8025
  3. [3] M. BRELOT, Lectures on Potential Theory, Tata Institute of Fundamental Research, Bombay, 1960 (reissued 1967). Zbl0257.31001
  4. [4] M. P. GAFFNEY, The Conservation Property of the Heat Equation on Riemannian Manifolds (Comm. Pure Appl. Math., 12, 1959, pp. 1-11). Zbl0102.09202MR21 #892
  5. [5] R. E. GREENE and H. WU, (a) On the Subharmonicity and Plurisubharmonicity of Geodesically Convex Functions (Indiana Univ. Math. J., 22, 1973, pp. 641-653) ; (b) Integrals of Subharmonic Functions on Manifolds of Nonnegative Curvature (Invent. Math., 27, 1974, pp. 265-298) ; (c) Approximation Theorems, C∞ Convex Exhaustions and Manifolds of Positive Curvature (Bull. Amer. Math. Soc., 81, 1975, pp. 101-104) ; (d) Whitney's Imbedding Theorem by Solutions of Elliptic Equations and Geometric Consequences (Proc. Symp. Pure Math., Vol. 27, part II, Amer. Math. Soc., Providence, R.I., 1975, pp. 287-296) ; (e) C∞ Convex Functions and Manifolds of Positive Curvature (Acta Math., 137, 1976, pp. 209-245) ; (f) On Kähler Manifolds of Positive Bisectional Curvature and a Theorem of Hartogs (Abh. Math. Sem., Univ. Hamburg, 47, 1978, pp. 171-185). MR54 #10672
  6. [6] M. HERVÉ, Analytic and Plurisubharmonic Functions in Finite and Infinite Dimensional Spaces (Lecture Notes in Math. No. 198, Springer-Verlag, Berlin-Heidelberg-New York, 1971). Zbl0214.36404MR57 #6479
  7. [7] R.-M. HERVÉ, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel (Ann. Ins. Fourier, Grenoble, 12, 1962, pp. 415-571). Zbl0101.08103MR25 #3186
  8. [8] M. HIRSCH, Differential Topology, Springer-Verlag, Berlin-Heidelberg-New York, 1976. Zbl0356.57001MR56 #6669
  9. [9] W. LITTMAN, A Strong Maximum Principle for Weakly L-Subharmonic Functions [J. Math. and Mech. (Indiana Univ. Math. J.) 8, 1959, pp. 761-770]. Zbl0090.08201MR21 #6468
  10. [10] J. R. MUNKRES, Elementary Differential Topology [Ann. Math. Studies, No. 54, Princeton Univ. Press, Princeton, N.J., (revised edition) 1966]. Zbl0161.20201MR33 #6637
  11. [11] R. RICHBERG, Stetige Streng Pseudoconvexe Funktionen (Math. Ann., 1975, 1968, pp. 257-286). Zbl0153.15401
  12. [12] S.-T. YAU, Some Function-Theoretic Properties of Complete Riemannian Manifolds and their Applications to Geometry (Indiana Univ. Math. J., 25, 1976, pp. 659-670). Zbl0335.53041MR54 #5502

Citations in EuDML Documents

top
  1. Helga Schirmer, Nielsen theory of transversal fixed point sets (with an appendix: C and C0 fixed point sets are the same, by R. E. Greene)
  2. R. E. Greene, K. Shiohama, Convex functions on complete noncompact manifolds : differentiable structure
  3. Atsushi Kasue, A compactification of a manifold with asymptotically nonnegative curvature
  4. Vicente Miquel, Vicente Palmer, Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications
  5. Zahra Sinaei, Riemannian Polyhedra and Liouville-Type Theorems for Harmonic Maps
  6. Atsushi Kasue, On a lower bound for the first eigenvalue of the Laplace operator on a riemannian manifold
  7. Jean-Pierre Demailly, Estimations L 2 pour l’opérateur ¯ d’un fibré vectoriel holomorphe semi-positif au-dessus d’une variété kählérienne complète
  8. Viorel Vâjâitu, Pseudoconvex domains over q -complete manifolds

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.