4 papers · 1 filter
Normal curvature bounds for immersions into Riemannian domains
Matteo Raffaelli
We study Gromov's problem on the minimal normal curvature of immersions. Our main result is a lower bound for the average normal curvature of a closed submanifold immersed in a Rie…
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…
Total torsion of three-dimensional lines of curvature
Matteo Raffaelli
A curve in a Riemannian manifold is three-dimensional if its torsion (signed second curvature function) is well-defined and all higher-order curvatures vanish identically.…
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…