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arXiv · 2010.11373

The Minkowski problem based on the (p,q)-mixed quermassintegrals

Bin Chen·Weidong Wang·Peibiao Zhao
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Abstract

Lutwak, Yang and Zhang [23] introduced the concept of Lp dual curvature measure for convex bodies and star bodies, and studied the Minkowski problem. We in this paper establish a new unified concept, in briefly, the (p,q)-mixed quermassintegrals, via (p,q)-dual mixed curvature measure, and further have a deep discussion on Minkowski problem with respect to the (p,q)-dual mixed curvature measure. By the way, we derive at some important properties and geometric inequalities for (p,q)-mixed quermassintegrals.

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Bin Chen, Weidong Wang, Peibiao Zhao. 2020-10-22. The Minkowski problem based on the (p,q)-mixed quermassintegrals. https://arxiv.org/abs/2010.11373

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