1 citations · 1 across the 3 of their papers we have counts for
9 papers
Smooth convex Bodies with proportional projection functions
Ralph Howard, Daniel Hug
For a convex body and , the function assigning to any -dimensional subspace of , the -dimensional volume of the orthogonal project…
A Generalized Affine Isoperimetric Inequality
Wenxiong Chen, Ralph Howard, Erwin Lutwak +2
A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric inequalities of plane convex geometry: The Blaschke-…
Convex Bodies of Constant Width and Constant Brightness
Ralph Howard
In 1926 S. Nakajima (= A. Matsumura) showed that any convex body in with constant width, constant brightness, and boundary of class is a ball. We show that the regular…
A general theory of almost convex functions
S. J. Dilworth, Ralph Howard, James W. Roberts
Let be the standard -dimensional simplex of non-negative tuples that sum to unity and let be a nonempty subset of . A real valued function defined on a…
Extremal Approximately Convex Functions and the Best Constants in a Theorem of Hyers and Ulam
S. J. Dilworth, Ralph Howard, James W. Roberts
Let and . A real-valued function defined on the -simplex is approximately convex with respect to iff f(\sum_{i=1}^B t_ix_i) \le \sum_{i=1}^B t…
Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables
Emil Cornea, Ralph Howard, Per-Gunnar Martinsson
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near poin…