Some Remarks on Harmonic Functions in Minkowski Spaces

Songting Yin
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Songting Yin: Department of Mathematics and Computer Science, Tongling University, Tongling 244000, China

Mathematics, 2019, vol. 7, issue 2, 1-8

Abstract: We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, if all harmonic functions have the mean value property or any function satisfying the mean value formula must be a harmonic function, then the Minkowski space is Euclidean.

Keywords: harmonic function; mean value formula; Minkowski spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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