3 citations · 4 across the 9 of their papers we have counts for
10 papers
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…
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{πr}{1 + \sqr…
Abelian subgroups of the fundamental group of a space with no conjugate points
James Dibble
Each Abelian subgroup of the fundamental group of a compact and locally simply connected -dimensional length space with no conjugate points is isomorphic to for s…
Totally geodesic maps into manifolds with no focal points
James Dibble
The set of totally geodesic representatives of a homotopy class of maps from a compact Riemannian manifold with nonnegative Ricci curvature into a complete Riemannian manifold…
Energy-minimizing maps from manifolds with nonnegative Ricci curvature
James Dibble
The energy of any representative of a homotopy class of maps from a compact and connected Riemannian manifold with nonnegative Ricci curvature into a complete Riemannian mani…
Central splitting of manifolds with no conjugate points
James Dibble
Each compact Riemannian manifold with no conjugate points admits a family of functions whose integrals vanish exactly when central Busemann functions split linearly. These function…
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…
The convexity radius of a Riemannian manifold
James Dibble
The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is pr…