82 citations · 182 across the 17 of their papers we have counts for
20 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…
Shur type comparison theorems for affine curves with application to lattice point estimates
Ralph Howard
If are two convex planar curve parameterized by affine arc length and is the area bounded by the restricti…
Bounding the number of lattice points near a convex curve by curvature
Ralph Howard, Ognian Trifonov
We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of o…
Total diameter and area of closed submanifolds
Mohammad Ghomi, Ralph Howard
The total diameter of a closed planar curve is the integral of its antipodal chord lengths. We show that this quantity is bounded below by twice the area of . Fur…
Normal curvatures of asymptotically constant graphs and Caratheodory's conjecture
Mohammad Ghomi, Ralph Howard
We show that Caratheodory's conjecture, on umbilical points of closed convex surfaces, may be reformulated in terms of the existence of at least one umbilic in the graphs of functi…
Tangent cones and regularity of real hypersurfaces
Mohammad Ghomi, Ralph Howard
We characterize embedded $\C^1$ hypersurfaces of as the only locally closed sets with continuously varying flat tangent cones whose measure-theoretic-multiplicity is at most…