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Cohomogeneity one Hermann actions and backward mean curvature flows

  • Kurando Baba
  • Naoyuki Koike
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Abstract

Principal orbits of cohomogeneity one Hermann actions form a natural class of equifocal hypersurfaces in symmetric spaces of compact type. Based on Kollross's classification of cohomogeneity one actions on irreducible symmetric spaces of compact type, we obtain the time evolution of the squared norm of the shape operator and the mean curvature along the long-time solution of the backward mean curvature flows starting from their principal orbits. These results explicitly describe the authors' previous generalization of the results of Liu-Terng on backward mean curvature flows of isoparametric hypersurfaces to this class of equifocal hypersurfaces.

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Cite

BibTeXRIS
BibTeX
@misc{baba2026cohomogeneity,
  title = {{Cohomogeneity one Hermann actions and backward mean curvature flows}},
  author = {Kurando Baba and Naoyuki Koike},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21884},
  eprint = {2610.21884},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21884},
}
RIS
TY  - UNPB
TI  - Cohomogeneity one Hermann actions and backward mean curvature flows
AU  - Kurando Baba
AU  - Naoyuki Koike
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21884
UR  - https://arxiv.org/abs/2610.21884
AB  - Principal orbits of cohomogeneity one Hermann actions form a natural class of equifocal hypersurfaces in symmetric spaces of compact type. Based on Kollross's classification of cohomogeneity one actions on irreducible symmetric spaces of compact type, we obtain the time evolution of the squared norm of the shape operator and the mean curvature along the long-time solution of the backward mean curvature flows starting from their principal orbits. These results explicitly describe the authors' previous generalization of the results of Liu-Terng on backward mean curvature flows of isoparametric hypersurfaces to this class of equifocal hypersurfaces.
ER  -