5 papers
Distortion from spheres into Euclidean spaces
James Dibble
Any function from a round -dimensional sphere of radius into -dimensional Euclidean space must distort the metric additively by at least $\displaystyle \frac{Ïr}{1 + \sq…
Mean curvature and closed geodesics in convex hypersurfaces
James Dibble, Joseph Ansel Hoisington
We give a sharp lower bound for the total mean curvature of a convex hypersurface in Euclidean space in terms of the length of a shortest nontrivial closed geodesic, generalizing a…
Area and antipodal distance in convex hypersurfaces
James Dibble, Joseph Hoisington
We establish a lower bound for the surface area of a closed, convex hypersurface in Euclidean space in terms of its displacement under continuous maps. As a result, a hypothesized…
The Yang indices of Grassmannians
James Dibble
An elementary combinatorial technique for computing lower bounds for the Yang indices of real Stiefel manifolds and oriented real Grassmannians is described. As a demonstration, it…
Heat flow within convex sets
James Dibble
A solution to the heat equation between Riemannian manifolds, where the domain is compact and possibly has boundary, will not leave a compact and locally convex set before the imag…