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\(C^\infty\) approximations of convex, subharmonic, and plurisubharmonic functions. (English) Zbl 0415.31001

MSC:
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
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References:
[1] L. AHLFORS and L. SARIO , Riemann Surfaces (Princeton Mathematical Series, N^\circ . 26, Princeton University Press, Princeton, N.J. 1960 ). MR 22 #5729 | Zbl 0196.33801 · Zbl 0196.33801
[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 ). MR 43 #8025 | Zbl 0223.53034 · Zbl 0223.53034
[3] M. BRELOT , Lectures on Potential Theory , Tata Institute of Fundamental Research, Bombay, 1960 (reissued 1967 ). Zbl 0257.31001 · Zbl 0257.31001
[4] M. P. GAFFNEY , The Conservation Property of the Heat Equation on Riemannian Manifolds (Comm. Pure Appl. Math., 12, 1959 , pp. 1-11). MR 21 #892 | Zbl 0102.09202 · Zbl 0102.09202
[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\infty 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\infty 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). MR 54 #10672 · Zbl 0235.53039
[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 ). MR 57 #6479 | Zbl 0214.36404 · Zbl 0214.36404
[7] R.-M. HERVÉ , Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel (Ann. Ins. Fourier, Grenoble, 12, 1962 , pp. 415-571). Numdam | MR 25 #3186 | Zbl 0101.08103 · Zbl 0101.08103
[8] M. HIRSCH , Differential Topology , Springer-Verlag, Berlin-Heidelberg-New York, 1976 . MR 56 #6669 | Zbl 0356.57001 · Zbl 0356.57001
[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]. MR 21 #6468 | Zbl 0090.08201 · Zbl 0090.08201
[10] J. R. MUNKRES , Elementary Differential Topology [Ann. Math. Studies, No. 54, Princeton Univ. Press, Princeton, N.J., (revised edition) 1966 ]. MR 33 #6637 | Zbl 0161.20201 · Zbl 0161.20201
[11] R. RICHBERG , Stetige Streng Pseudoconvexe Funktionen (Math. Ann., 1975 , 1968 , pp. 257-286). Zbl 0153.15401 · Zbl 0153.15401
[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). MR 54 #5502 | Zbl 0335.53041 · Zbl 0335.53041
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