5 papers
A quantitative Schur comparison theorem for curves in CAT(k) spaces
Mohammad Ghomi, John Ioannis Stavroulakis
We obtain a quantitative form of Schur's comparison theorem for curves with finite total curvature in CAT(k) spaces. This sharpens and extends the classical arm and bow lemmas in E…
-Principles for smooth curves and knots with prescribed curvature
Mohammad Ghomi, Matteo Raffaelli
We show that smooth curves with prescribed curvature satisfy a -dense -principle in the space of immersed curves in Euclidean space. More precisely, every cur…
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…
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 on negatively curved surfaces in Euclidean -space. In particu…
-Principles for curves and knots of constant torsion
Mohammad Ghomi, Matteo Raffaelli
We prove that curves of constant torsion satisfy the -dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant tors…