Normal curvature of immersed tori of dimension at most $18$

Matteo Raffaelli

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arXiv · 2608.13726

Normal curvature of immersed tori of dimension at most $18$

Matteo Raffaelli

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Abstract

We prove that if the $n$-dimensional torus $T^n$ is smoothly immersed in the unit ball $B^q\subset\mathbb R^q$ and $n\leq 18$, then there exists a point at which the spherical average of $\lvert II(u,u)\rvert^2$ is at least $3n/(n+2)$. This answers a question of Petrunin in these dimensions. The proof combines the scalar-curvature obstruction for the torus with a conformal-Laplacian argument.

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BibTeX RIS

Matteo Raffaelli. 2026-08-13. Normal curvature of immersed tori of dimension at most $18$. https://arxiv.org/abs/2608.13726

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