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math.DG2025
Riemannian 3-spheres that are hard to sweep out by short curves
Omar Alshawa, Herng Yi Cheng
We construct a family of Riemannian 3-spheres that cannot be "swept out" by short closed curves. More precisely, for each we construct a Riemannian 3-sphere with diamet…
math.DG2024
Stable closed geodesics and stable figure-eights in convex hypersurfaces
Herng Yi Cheng
For each odd , we construct a closed convex hypersurface of that contains a non-degenerate closed geodesic with Morse index zero. A classical theorem o…