7 papers
Total curvature and isoperimetric inequalities in pinched Cartan-Hadamard manifolds
Mohammad Ghomi
We establish a sharp lower bound for the total Gauss-Kronecker curvature of convex hypersurfaces in Cartan-Hadamard manifolds with pinched negative curvature. The bound holds in al…
Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity
Mohammad Ghomi
Using the Chern-Gauss-Bonnet theorem, we establish a sharp inequality for the total Gauss-Kronecker curvature of convex hypersurfaces in Cartan-Hadamard manifolds with nullit…
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…
Continuity of total curvatures of Riemannian hypersurfaces
Mohammad Ghomi
We show that total generalized mean curvatures of hypersurfaces with positive reach in Riemannian manifolds, and convex bodies in Cartan-Hadamard spaces, are continuous with respec…
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…
Convexity and rigidity of hypersurfaces in Cartan-Hadamard manifolds
Mohammad Ghomi
We show that in Cartan-Hadamard manifolds , , closed infinitesimally convex hypersurfaces bound convex flat regions, if curvature of vanishes on tangent pl…