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| 摘要: |
| 本文研究了Lp-Minkowski问题（解是中心在原点的椭球的假定下）.利用支撑函数与高斯曲率的关系，获得了当p < 1时椭球解的唯一性，推广了Lp-Minkowski问题以及Lp-和的Christoffel-Minkowski问题的唯一性结果. |
| 关键词: 唯一性 Minkowski问题 Monge-Ampère方程 k-Hessian方程 |
| DOI： |
| 分类号:O175.25;O186.12 |
| 基金项目: |
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| ON THE UNIQUENESS OF ELLIPSOID SOLUTIONS TO THE Lp-MINKOWSKI PROBLEM |
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LI Si-yuan
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| Abstract: |
| In this paper, we study the Lp-Minkowski problem (under the assumption that the solutions are ellipsoids centered at the origin). Through the relation between support function and Gauss curvature, we obtain the uniqueness of ellipsoid solutions for p < 1, and generalize the uniqueness result for Lp-Minkowski problem and Christoffel-Minkowski problem of Lp-sum. |
| Key words: uniqueness Minkowski problem Monge-Ampère equation k-Hessian equation |
