Mohammad Ghomi

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20242026

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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 $C^{α \geq 2}$ cur…

math.DG2025

A local isoperimetric inequality for balls with nonpositive curvature

Mohammad Ghomi, John Ioannis Stavroulakis

We show that small perturbations of the metric of a ball in Euclidean n-space to metrics with nonpositive curvature do not reduce the isoperimetric ratio. Furthermore, the isoperim…

h-Principles for smooth curves and knots with prescribed curvature

A local isoperimetric inequality for balls with nonpositive curvature

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