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math.DG2026
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…
math.DG2026
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…
math.DG2025
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…