Mohammad Ghomi

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20242026

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math.DG2024

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 $Γ$ on negatively curved surfaces $M$ in Euclidean $3$ -space. In particu…

math.DG2024

$h$ -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…

Topology of closed asymptotic curves on negatively curved surfaces

h-Principles for curves and knots of constant torsion

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