54 citations · 210 across the 33 of their papers we have counts for
5 papers · 1 filter
Geometric structures and the Laplace spectrum, part II
Samuel Lin, Benjamin Schmidt, Craig Sutton
We continue our exploration of the extent to which the spectrum encodes the local geometry of a locally homogeneous three-manifold and find that if and are a pair o…
Preserve one, preserve all
Meera Mainkar, Benjamin Schmidt
Isometries of metric spaces preserve all level sets of . We formulate and prove cases of a conjecture asserting if is a complete Riemannian manifold, then a function…
Geometric structures and the Laplace spectrum
Samuel Lin, Benjamin Schmidt, Craig Sutton
Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is dete…
Diameters of Ball Intersections
Meera Mainkar, Benjamin Schmidt
We prove the diameter of the intersection of two closed convex balls in a Riemannian manifold eventually decreases continuously as the centers of the balls move apart.
Characterizing Round Spheres Using Half-Geodesics
Ian M Adelstein, Benjamin Schmidt
A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this note establishes th…