The dual Minkowski problem for negative indices

Yiming Zhao New York University

Convex and Discrete Geometry mathscidoc:1703.40010

Calc. Var. Partial Differential Equations, 56, (2), 18, 2017
Recently, the duals of Federer’s curvature measures, called dual curvature measures, were discovered by Huang, Lutwak, Yang & Zhang (ACTA, 2016). In the same paper, they posed the dual Minkowski problem, the characterization problem for dual curvature measures, and proved existence results when the index, q, is in (0,n). The dual Minkowski problem includes the Aleksandrov problem (q = 0) and the logarithmic Minkowski problem (q = n) as special cases. In the current work, a complete solution to the dual Minkowski problem whenever q < 0, including both existence and uniqueness, is presented.
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  title={The dual Minkowski problem for negative indices},
  author={Yiming Zhao},
  booktitle={Calc. Var. Partial Differential Equations},
Yiming Zhao. The dual Minkowski problem for negative indices. 2017. Vol. 56. In Calc. Var. Partial Differential Equations. pp.18.
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