Rigidity of balls in the solid mean value property for polyharmonic functions

Nicola Abatangelo

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arXiv · 2603.09409

Rigidity of balls in the solid mean value property for polyharmonic functions

Nicola Abatangelo

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Abstract

We show that balls are the only open bounded domains for which the mean value formula for polyharmonic functions holds. We do so by adapting an argument of \"U. Kuran for harmonic functions. Also, we provide a quantitative version of the same result.

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Nicola Abatangelo. 2026-03-10. Rigidity of balls in the solid mean value property for polyharmonic functions. https://arxiv.org/abs/2603.09409

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