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arXiv · 2610.22229

Observing minimal submanifolds with isolated singularities on open sets of metrics

Alessandro Carlotto·Yangyang Li·Zhihan Wang
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Abstract

We develop a perturbative theory for minimal submanifolds with only (strongly) isolated singularities, with respect to varying background Riemannian metrics. As an application, we obtain a general "sporadic persistence" criterion, thus naturally complementing the non-persistence theorem by the authors. In particular, such a criterion is satisfied by the spherical suspension in $\mathbb{S}^{3m+2}$ of the Veronese embedding of $\mathbb{K}\mathbb{P}^2$ for $\mathbb{K}=\mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O}$ (the normed division algebras) in the round spheres of dimension $3m+1=4,7,13,25$ respectively, thereby providing families of continuously varying $(2m+1)$-dimensional stationary varifolds with isolated singularities that are observable on an open set of metrics. By our previous results, these phenomena cannot possibly occur in the codimension one scenario.

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Alessandro Carlotto, Yangyang Li, Zhihan Wang. 2026-10-15. Observing minimal submanifolds with isolated singularities on open sets of metrics. https://arxiv.org/abs/2610.22229

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