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Riemannian convex bodies with a geodesic segment on the boundary

  • Hongda Qiu
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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.

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Cite

BibTeXRIS
BibTeX
@misc{qiu2026riemannian,
  title = {{Riemannian convex bodies with a geodesic segment on the boundary}},
  author = {Hongda Qiu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02355},
  eprint = {2611.02355},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02355},
}
RIS
TY  - UNPB
TI  - Riemannian convex bodies with a geodesic segment on the boundary
AU  - Hongda Qiu
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02355
UR  - https://arxiv.org/abs/2611.02355
AB  - 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.
ER  -