On the regularity of the solution of the n‐dimensional Minkowski problem

@inproceedings{Cheng1976OnTR,
  title={On the regularity of the solution of the n‐dimensional Minkowski problem},
  author={Shiu-Yuen Cheng and Shing-Tung Yau},
  year={1976}
}
where xi are the coordinate functions on S". Minkowski then asked the converse of the problem. Namely, given a positive function K defined on S" satisfying the above integral conditions, can we find a closed strictly convex hypersurface whose curvature function is given by K? Minkowski solved the problem in the category of polyhedrons. Then A. D. Alexandrov and others solved the problem in general. However, this last solution does not provide any information about the regularity of the (unique… CONTINUE READING

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