PreprintCC BY 4.0arXiv
Immersed hypersurfaces with positive first Newton transformation
Abstract
We prove that every closed cooriented hypersurface immersion in Rn+1, n≥ 2, with positive definite first Newton transformation bounds a compact immersed manifold with the prescribed boundary map and outward coorientation. Combined with the rigidity results of Ros and Pinkall, this filling theorem implies that every closed connected hypersurface immersed in Rn+1 with constant scalar curvature is a round sphere.
Related
- Sphere Theorems for Immersed Hypersurfaces with Constant Scalar Curvature
- Regularity of branched stable minimal immersed hypersurfaces
- On the Factored Newton Iteration for Positive-Real Algebraic Riccati Equations via the Matrix Sign Function
- Completion Fibres of Infinite Positive Newton Conformal Metrics Near Corners
- First-Passage Time Problems for Jump-Diffusion Processes with Positive and Negative Jumps
BibTeX
@misc{you2026immersed,
title = {{Immersed hypersurfaces with positive first Newton transformation}},
author = {Jiangcheng You and Heng Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26665},
eprint = {2609.26665},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26665},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Immersed hypersurfaces with positive first Newton transformation
AU - Jiangcheng You
AU - Heng Zhang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26665
UR - https://arxiv.org/abs/2609.26665
AB - We prove that every closed cooriented hypersurface immersion in R^n+1, n≥ 2, with positive definite first Newton transformation bounds a compact immersed manifold with the prescribed boundary map and outward coorientation. Combined with the rigidity results of Ros and Pinkall, this filling theorem implies that every closed connected hypersurface immersed in R^n+1 with constant scalar curvature is a round sphere.
ER -