On the continuity of the solution to the Minkowski problem for Lp torsional measure
On the continuity of the solution to the Minkowski problem for Lp torsional measure
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DOI：
10.2298/fil2308387l
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发表时间：
2023
期刊：
影响因子：
0.8
通讯作者：
Ni Li;Shuang Mou
中科院分区：
文献类型：
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作者：
Ni Li;Shuang Mou
本文研究了 Lp 扭转量度 Minkowski 问题解的连续性。对于 p ? (1, n + 2) ? (n + 2,?)，我们证明，如果 Lp 扭转测度序列（与这些凸体相关）弱收敛，则 Rn 中的凸体序列在 Hausdorff 度量中是收敛的。此外，我们还证明了 Lp 扭转量度的 Minkowski 问题的解对于 p 是连续的。
This paper deals with on the continuity of the solution to the Minkowski problem for Lp torsional measure. For p ? (1, n + 2) ? (n + 2,?), we show that a sequence of convex bodies in Rn is convergent in Hausdorff metric if the sequence of the Lp torsional measures (associated with these convex bodies) is weakly convergent. Moreover, we also prove that the solution to the Minkowski problem for Lp torsional measure is continuous with respect to p.