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PreprintarXiv licencearXiv

Scalar--Mean Rigidity for Hyperbolic Balls in Dimensions 2≤ n≤ 5

  • Chenghang Lu
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Abstract

In this paper, we prove the non-spin hyperbolic scalar--mean rigidity theorem in dimensions 2≤ n≤5, resolving the corresponding low-dimensional case of a problem of Gromov. The proof combines the Jang deformation with capillary μ-bubble dimension reduction. We also establish weighted scalar--mean rigidity for Euclidean ball--torus products in total dimension at most seven and show that its hyperbolic analogue fails.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026scalarmean,
  title = {{Scalar--Mean Rigidity for Hyperbolic Balls in Dimensions $2\le n\le 5$}},
  author = {Chenghang Lu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29488},
  eprint = {2610.29488},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29488},
}
RIS
TY  - UNPB
TI  - Scalar--Mean Rigidity for Hyperbolic Balls in Dimensions 2≤ n≤ 5
AU  - Chenghang Lu
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29488
UR  - https://arxiv.org/abs/2610.29488
AB  - In this paper, we prove the non-spin hyperbolic scalar--mean rigidity theorem in dimensions 2≤ n≤5, resolving the corresponding low-dimensional case of a problem of Gromov. The proof combines the Jang deformation with capillary μ-bubble dimension reduction. We also establish weighted scalar--mean rigidity for Euclidean ball--torus products in total dimension at most seven and show that its hyperbolic analogue fails.
ER  -