4 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…
Total absolute curvature and rigidity of surfaces in Cartan-Hadamard manifolds
Mohammad Ghomi, Joseph Ansel Hoisington, Matteo Raffaelli +1
We show that closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies. This generalizes Chern-Lashof's theorem for surfaces in…
Energy-minimizing Mappings of Complex Projective Spaces
Joseph Hoisington
We show that in all homotopy classes of mappings from complex projective space to Riemannian manifolds, the infimum of the energy is proportional to the infimal area in the homotop…
Energy-minimizing mappings of real projective spaces
Joseph Hoisington
We give a sharp lower bound for the energy in homotopy classes of mappings from real projective space to Riemannian manifolds, together with an upper bound for its infimum. We char…