7 citations · 10 across the 8 of their papers we have counts for
4 papers · 1 filter
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…
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 curvature of convex hypersurfaces in Cartan-Hadamard manifolds
Mohammad Ghomi, John Ioannis Stavroulakis
We show that if the curvature of a Cartan-Hadamard -manifold is constant near a convex hypersurface , then the total Gauss-Kronecker curvature is not less th…
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…