论文标题
平面的直径估计$ L_P $ DUAL MINKOWSKI问题
Diameter estimate for planar $L_p$ dual Minkowski problem
论文作者
论文摘要
在本文中，给定对$ \ mathbb {s}^1 $的规定措施，其密度有限且积极，我们为平面$ l_p $ l_p $ dual minkowski问题建立了统一的直径估算，当$ 0 <p <1 $ <1 $和$ q \ q \ ge 2 $。当测量的密度足够接近$ c^α$时，我们还证明了解决方案对$ L_P $ Minkowski问题的独特性和积极性。
In this paper, given a prescribed measure on $\mathbb{S}^1$ whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar $L_p$ dual Minkowski problem when $0<p<1$ and $q\ge 2$. We also prove the uniqueness and positivity of solutions to the $L_p$ Minkowski problem when the density of the measure is sufficiently close to a constant in $C^α$.
