Continuity of the solution to the 𝐿_{𝑝} Minkowski problem

Zhu, Guangxian

doi:10.1090/proc/13248

Continuity of the solution to the $L_{p}$ Minkowski problem
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Proc. Amer. Math. Soc. 145 (2017), 379-386 Request permission

Abstract:

For $p>1$ with $p\neq n$, it is proved that the weak convergence of $L_{p}$ surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric and that the solution to the $L_{p}$ Minkowski problem is continuous with respect to $p$.

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