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Mean curvature flow with linear oblique derivative boundary conditions

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Abstract

In this paper, we study the mean curvature flow with oblique derivative boundary conditions. We prove the longtime existence by choosing a suitable auxiliary function. Also, we prove the asymptotic behavior of the mean curvature flow with zero oblique derivative boundary data which is a generalization of Huisken’s original result about prescribed perpendicular contact angle.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11471188). The first author shows his thanks to Professor Xinan Ma for his constant encouragements and some helpful discussions on the topic of oblique derivative boundary value problems.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Peihe Wang & Yuna Zhang

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  1. Peihe Wang
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  2. Yuna Zhang
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Correspondence to Peihe Wang.

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Wang, P., Zhang, Y. Mean curvature flow with linear oblique derivative boundary conditions. Sci. China Math. 65, 1413–1430 (2022). https://doi.org/10.1007/s11425-020-1795-2

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  • DOI: https://doi.org/10.1007/s11425-020-1795-2

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