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Mean value property and harmonic functions. (English) Zbl 0863.31012
GowriSankaran, K. (ed.) et al., Classical and modern potential theory and applications. Proceedings of the NATO advanced research workshop, Chateau de Bonas, France, July 25–31, 1993. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 430, 359-398 (1994).
This is an excellent and comprehensive survey on the spherical and volume mean value properties of harmonic and closely related functions. It is rich in historical remarks and quotations. Its extensive list of references covers more than twelve pages, and provides an extremely useful guide to the literature, both classical and modern. The topics covered include the standard mean value properties, their converses, two radius theorems, restricted mean value properties, inverse mean value properties, and asymptotic mean value properties.
For the entire collection see [Zbl 0856.00022].

31C05 Harmonic, subharmonic, superharmonic functions on other spaces
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
35K05 Heat equation