82 citations · 106 across the 26 of their papers we have counts for
38 papers
A Converse to the Archimedes Sphere Theorem
Mohammad Ghomi, Ralph Howard, Mijia Lai
We show that a convex surface in Euclidean 3-space is a sphere if the area cut off from it by a slab of some fixed width depends only on the direction of the slab. This result gene…
The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds
Shibing Chen, Mohammad Ghomi, Peng Wang
We show that the sharp Euclidean isoperimetric inequality holds for domains in complete simply connected Riemannian -manifolds of nonpositive sectional curvature, …
The Cartan-Hadamard conjecture in dimension five
Shibing Chen, Mohammad Ghomi, Peng Wang
We show that the sharp Euclidean isoperimetric inequality holds for domains in complete simply connected Riemannian -manifolds of nonpositive sectional curvature, which establis…
Mean curvatures and symmetry of convex hypersurfaces
Mohammad Ghomi
Let be a closed convex hypersurface in Euclidean space, and be its th mean curvature. We show that is symmetric with respect to a hyperplane orthogonal to…
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…