From the 1 of 3 linked papers with an AI index.
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Normal curvature bounds for immersions into Riemannian domains
Matteo Raffaelli
The paper establishes a lower bound for the average normal curvature of closed submanifolds immersed in Riemannian domains, using an invariant that captures optimal n‑trace convexi…
Total absolute curvature and rigidity of surfaces in Cartan-Hadamard manifolds
Mohammad Ghomi, Joseph Ansel Hoisington, Matteo Raffaelli +1
We show that closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies. This generalizes Chern-Lashof's theorem for surfaces in…
The convex hull of a convex space curve with four vertices
Jakob Bohr, Steen Markvorsen, Matteo Raffaelli
We obtain an upper bound for the volume of the convex hull of a simple closed Frenet curve with exactly four vertices, i.e., four points of vanishing torsion, and lying on the boun…
The geometric Cauchy problem for rank-one submanifolds
Matteo Raffaelli
Given a smooth distribution of -dimensional planes along a smooth regular curve in , we consider the following problem: to find an -dimen…
Existence of optimal flat ribbons
Simon Blatt, Matteo Raffaelli
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in can be extended to an infinitely narrow flat ribbon having mini…