1 citations · 1 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…
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 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…
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…
Calibrations and Energy-Minimizing Mappings of Rank-1 Symmetric Spaces
Joseph Hoisington
We prove lower bounds for energy functionals of mappings from real, complex and quaternionic projective spaces to Riemannian manifolds. For real and complex projective spaces, thes…
Hypersurfaces, Geodesics and Isoperimetric Inequalities in Cartan-Hadamard Manifolds
Joseph Hoisington
We prove an inequality for submanifolds of Cartan-Hadamard manifolds, which relates the geometry of a submanifold to the measure of the geodesics in the ambient space which it inte…
Symmetry and Isoperimetry for Riemannian Surfaces
Joseph Ansel Hoisington, Peter McGrath
For a domain in a geodesically convex surface, we introduce a scattering energy , which measures the asymmetry of by quantifying its incompatibility with an…
Steiner's formula and a variational proof of the isoperimetric inequality
Joseph Ansel Hoisington
We give a new proof of the isoperimetric inequality in the plane, based on Steiner's formula for the area of a convex neighborhood. This proof establishes the isoperimetric inequal…
On the Total Curvature and Betti Numbers of Complex Projective Manifolds
Joseph Ansel Hoisington
We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose tot…
Making matrices better: Geometry and topology of polar and singular value decomposition
Dennis DeTurck, Amora Elsaify, Herman Gluck +4
Our goal here is to see the space of matrices of a given size from a geometric and topological perspective, with emphasis on the families of various ranks and how they fit together…