Author

Matteo Raffaelli

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Preprint Aug 2026

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

For $n\leq 18$, we prove that any smooth immersion of the $n$-torus into the closed unit ball in $\mathbb R^q$ has a point at which the spherical average of $\lvert II(v,v)\rvert^2$ is at least $3n/(n+2)$. This answers a question of Petrunin in these dimensions. The proof combines the scalar curvature obstruction for t...

Matteo Raffaelli · 1 citation

Preprint Aug 2026

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

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 scal...

Matteo Raffaelli · 1 citation