Year: 2026
Type: preprint
Abstract: We construct compact convex bodies whose boundaries contain a nontrivial geodesic segment and are strictly convex elsewhere. The construction applies if sectional curvature is constant near a point, or if a normal Jacobi operator has a simple maximal eigenvalue. In particular, such a body exists in every smooth three-dimensional or four-dimensional Riemannian manifold.
Source: arXiv (Cornell University)
Author: Qiu, Hongda
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225188220