5 citations
2 papers
cs.CG2021★ 5 cited
Continuous Flattening of All Polyhedral Manifolds using Countably Infinite Creases
Zachary Abel, Erik D. Demaine, Martin L. Demaine +4
We prove that any finite polyhedral manifold in 3D can be continuously flattened into 2D while preserving intrinsic distances and avoiding crossings, answering a 19-year-old open p…
math.DG2019★ 1 cited
The structure of the conjugate locus of a general point on ellipsoids and certain Liouville manifolds
Jin-ichi Itoh, Kazuyoshi Kiyohara
It is well known since Jacobi that the geodesic flow of the ellipsoid is "completely integrable", which means that the geodesic orbits are described in a certain explicit way. Howe…