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A remark on the existence of sphere with prescribed mean curvature

Shing-Tung Yau

Differential Geometry mathscidoc:1912.43649

Asian Journal of Mathematics, 1, (2), 293-294, 1997.6
In 1976, the author (see the open problem section in [3]) asked the following question: if p is a function defined on i? 3, what is the condition on p so that there is a sphere in R3 whose mean curvature is given by p. There were important works by Treibergs-Wei [2] and others on this question. Recently in a lecture that I gave in the Chinese University of Hong Kong, I realized that my work with R. Schoen on the existence of black hole can be used to settle the prescribed mean curvature question for a large class of p.
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@inproceedings{shing-tung1997a,
  title={A remark on the existence of sphere with prescribed mean curvature},
  author={Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204728581506213},
  booktitle={Asian Journal of Mathematics},
  volume={1},
  number={2},
  pages={293-294},
  year={1997},
}
Shing-Tung Yau. A remark on the existence of sphere with prescribed mean curvature. 1997. Vol. 1. In Asian Journal of Mathematics. pp.293-294. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204728581506213.
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