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arXiv · 2608.22225

Stable constant weighted mean curvature hypersurfaces in anti-Gaussian space

Jinchuan Bai·Chao Xia
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Abstract

We prove that in the anti-Gaussian space $\bigl(\R^{m+1},\bar g_{\Euc},e^{|x|^2/4}\,dx\bigr)$, $m\ge2$, round spheres centered at the origin are the only closed, connected, two-sided immersed hypersurfaces with constant weighted mean curvature that are stable under weighted-volume-preserving variations.

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Jinchuan Bai, Chao Xia. 2026-08-23. Stable constant weighted mean curvature hypersurfaces in anti-Gaussian space. https://arxiv.org/abs/2608.22225

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