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arXiv · 1703.00524

The dual Minkowski problem for negative indices

Yiming Zhao
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Abstract

Recently, the duals of Federer's curvature measures, called dual curvature measures, were discovered by Huang, Lutwak, Yang, and 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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Yiming Zhao. 2017-03-01. The dual Minkowski problem for negative indices. https://doi.org/10.1007/s00526-017-1124-x

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