From the 1 of 5 linked papers with an AI index.
5 papers
A quantitative Schur comparison theorem for curves in CAT(k) spaces
Mohammad Ghomi, John Ioannis Stavroulakis
The paper provides a quantitative version of Schur's comparison theorem for curves with finite total curvature in CAT(k) spaces, extending classic results from Euclidean and Rieman…
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…
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…
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…
Dimension estimates for nonlinear nonautonomous systems in arbitrary normed spaces
John Ioannis Stavroulakis
We calculate explicit estimates for the dimension of trajectories satisfying a certain growth bound. We generalize the classic results of Kurzweil by considering nonlinear nonauton…