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Obata theorem of σk-flat and constant associated kth boundary curvature equation
Abstract
On the upper hemisphere, we use the Obata-Escobar argument to establish an Obata theorem for σk-flat and positive constant boundary ℬk-curvature equation, which was initiated by Case-Wang [Adv. Math. 337 (2018), 83-106].
Related
- Liouville Theorem for the Constant Q/R-Curvature Equation
- Constant mean curvature disks with circular boundary
- Constant mean curvature disks with circular boundary in the $3$-sphere and in hyperbolic space
- Hopf type theorem for surfaces of constant weighted mean curvature in Riemannian manifolds
- Stable constant mean curvature disks with circular boundary in homogeneous three-manifolds
BibTeX
@misc{chen2026obata,
title = {{Obata theorem of $σ_k$-flat and constant associated $k$th boundary curvature equation}},
author = {Xuezhang Chen and Wei Wei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34835},
eprint = {2609.34835},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34835},
}
RIS
TY - UNPB
TI - Obata theorem of σ_k-flat and constant associated kth boundary curvature equation
AU - Xuezhang Chen
AU - Wei Wei
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34835
UR - https://arxiv.org/abs/2609.34835
AB - On the upper hemisphere, we use the Obata-Escobar argument to establish an Obata theorem for σ_k-flat and positive constant boundary ℬ_k-curvature equation, which was initiated by Case-Wang [Adv. Math. 337 (2018), 83-106].
ER -