Remarks on topology of stable translating solitons

  • Keita KunikawaEmail author
  • Shunsuke Saito
Original Paper


We show that any complete f-stable translating soliton M admits no codimension one cycle which does not disconnect M. As a corollary, it follows that any two dimensional complete f-stable translating soliton has genus zero.


Translating solitons Stability Weighted harmonic forms 

Mathematics Subject Classification (2010)

Primary: 53C42 Secondary: 53C21 



The first author would like to thank Miyuki Koiso and Reiko Miyaoka for their valuable comments and discussion on stability of translators. The second author was supported by Structural Materials for Innovation Strategic Innovation Promotion Program D72.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Advanced Institute for Materials ResearchTohoku UniversitySendaiJapan

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