Abstract
We study the stability of unduloids with free boundary in the domain B between two parallel hyperplanes in Rn+1. If the unduloid has one half of period in B and is sufficiently close to a cylinder, then for 2 ≤ n ≤ 10, it is unstable; while for n ≥ 11, it is stable. If the unduloid has two or more halves of period in B and is sufficiently close to a cylinder, then for all n ≥ 2, it is unstable.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11271214 and 11671224) and Ben Andrews’ ARC Laureate Fellowship (Grant No. FL150100126). The authors thank the referees for careful reading of the paper and many valuable suggestions and comments which made this paper better and more readable. The first and third authors are also grateful to Prof. Ben Andrews for his continuous help.
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Li, H., Xia, Y. & Xiong, C. Stability of unduloid bridges with free boundary in a Euclidean slab. Sci. China Math. 61, 917–928 (2018). https://doi.org/10.1007/s11425-016-9076-9
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DOI: https://doi.org/10.1007/s11425-016-9076-9