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arXiv · 2603.25231

A spherical flatness index and a stability inequality for harmonic pseudospheres

Andrea Buffoni·Giovanni Cupini·Ermanno Lanconelli
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Abstract

We introduce a new flatness index for the boundary of an open subset $\Omega$ of $\mathbb{R}^n$, $n\ge 2$. This index provides a necessary condition for $\partial\Omega$ to be a harmonic pseudosphere and sufficient conditions for a harmonic pseudosphere to be a Euclidean sphere. These conditions will follow from a stability inequality formulated in terms of a harmonic invariant, the Kuran gap, recently introduced by the last two authors.

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Andrea Buffoni, Giovanni Cupini, Ermanno Lanconelli. 2026-03-26. A spherical flatness index and a stability inequality for harmonic pseudospheres. https://arxiv.org/abs/2603.25231

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