### Abstract

Let S be a smooth hypersurface properly embedded in R^{N} with N ≥ 3 and consider its tubular neighborhood N .We show that, if a heat flow over N with appropriate initial and boundary conditions has S as a stationary isothermic surface, then S must have some sort of symmetry.

Original language | English |
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Title of host publication | Geometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015 |

Editors | Carlo Nitsch, Filippo Gazzola, Kazuhiro Ishige, Paolo Salani |

Publisher | Springer New York LLC |

Pages | 231-239 |

Number of pages | 9 |

ISBN (Print) | 9783319415369 |

DOIs | |

Publication status | Published - 2016 Jan 1 |

Event | Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015 - Palinuro, Italy Duration: 2015 May 25 → 2015 May 29 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 176 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015 |
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Country | Italy |

City | Palinuro |

Period | 15/5/25 → 15/5/29 |

### Keywords

- Cauchy problem
- Heat equation
- Initial-boundary value problem
- Stationary isothermic surface
- Symmetry
- Tubular neighborhood

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Sakaguchi, S. (2016). Symmetry problems on stationary isothermic surfaces in euclidean spaces. In C. Nitsch, F. Gazzola, K. Ishige, & P. Salani (Eds.),

*Geometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015*(pp. 231-239). (Springer Proceedings in Mathematics and Statistics; Vol. 176). Springer New York LLC. https://doi.org/10.1007/978-3-319-41538-3_13