Matteo Raffaelli

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math.DG2026

A mechanical characterization of constant mean curvature surfaces

Matteo Raffaelli

The speed of a ball rolling without skidding or spinning on a surface $S$ is the length of the velocity of its center. We show that if the speed depends only on $p \in S$ , then $S$ …

math.DG2025

The geometric Cauchy problem for constant-rank submanifolds

Matteo Raffaelli

Given a smooth $s$ -dimensional submanifold $S$ of $R^{m + c}$ and a smooth distribution $D \supset T S$ of rank $m$ along $S$ , we study the following geometric Cauchy problem:…

math.DG2025

$h$ -Principles for smooth curves and knots with prescribed curvature

Mohammad Ghomi, Matteo Raffaelli

We show that smooth curves with prescribed curvature satisfy a $C^{1}$ -dense $h$ -principle in the space of immersed curves in Euclidean space. More precisely, every $C^{I^\pm \geq 2}$ cu…

math.DG2025

$h$ -Principles for curves and knots of constant torsion

Mohammad Ghomi, Matteo Raffaelli

We prove that curves of constant torsion satisfy the $C^{1}$ -dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant tors…

math.DG2025

Topology of closed asymptotic curves on negatively curved surfaces

Mohammad Ghomi, Matteo Raffaelli

Motivated by Nirenberg's problem on isometric rigidity of tight surfaces, we study closed asymptotic curves $I^$ on negatively curved surfaces $M$ in Euclidean $3$ -space. In partic…

math.DG2025

Deformations of curves with constant curvature

Mohammad Ghomi, Matteo Raffaelli

We prove that curves of constant curvature satisfy the parametric $C^{1}$ -dense relative $h$ -principle in the space of immersed curves with nonvanishing curvature in Euclidean space…

A mechanical characterization of constant mean curvature surfaces

The geometric Cauchy problem for constant-rank submanifolds

h-Principles for smooth curves and knots with prescribed curvature

h-Principles for curves and knots of constant torsion

Topology of closed asymptotic curves on negatively curved surfaces

Deformations of curves with constant curvature

$h$ -Principles for smooth curves and knots with prescribed curvature

$h$ -Principles for curves and knots of constant torsion