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Mathematics 2019, 7(2), 196; https://doi.org/10.3390/math7020196

Some Remarks on Harmonic Functions in Minkowski Spaces

Department of Mathematics and Computer Science, Tongling University, Tongling 244000, China
Received: 16 December 2018 / Revised: 15 February 2019 / Accepted: 15 February 2019 / Published: 19 February 2019
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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. View Full-Text
Keywords: harmonic function; mean value formula; Minkowski spaces harmonic function; mean value formula; Minkowski spaces
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Yin, S. Some Remarks on Harmonic Functions in Minkowski Spaces. Mathematics 2019, 7, 196.

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