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Remarks on area maximizing hypersurfaces over \({{\pmb {\mathbb {R}}}}^n\backslash \{0\}\) and exterior domains

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Abstract

In this note, we provide a complete classification for the entire area maximizing hypersurfaces with an isolated singularity. We also construct an interesting illustrated example. For the area maximizing hypersurfaces over exterior domains, we obtain a partial result on their asymptotic behavior at infinity. We also establish the solvability of the exterior Dirichlet problems for the area maximizing hypersurfaces.

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Acknowledgements

The author would like to thank Professor Yu Yuan for many helpful discussions on this work. This paper was completed during the author’s visit to University of Washington (Seattle). His visit was funded by China Scholarship Council. He would also like to thank Professor Yu Yuan for the invitation and to the Department of Mathematics for warm hospitality. The author also would like to thank the anonymous referee for useful comments and suggestions.

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  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Guanghao Hong

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  1. Guanghao Hong
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Correspondence to Guanghao Hong.

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Hong, G. Remarks on area maximizing hypersurfaces over \({{\pmb {\mathbb {R}}}}^n\backslash \{0\}\) and exterior domains. manuscripta math. 162, 473–481 (2020). https://doi.org/10.1007/s00229-019-01139-4

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  • DOI: https://doi.org/10.1007/s00229-019-01139-4

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