A. R. Martínez Fernández obtained upper bounds for quermassintegrals of the p-inner parallel bodies: an extension of the classical inner parallel body to the $L_p$ -Brunn-Minkowski theory. In this paper, we establish (sharp) upper and lower bounds for quermassintegrals of p-inner parallel bodies. Moreover, the sufficient and necessary conditions of the equality case for the main inequality are obtained, which characterize the so-called tangential bodies.

中文翻译：

---

p内平行体的进一步不等式和性质

AR Martínez Fernández 获得了p内平行体的 quermassintegrals 的上限：经典内平行体对 $L_p$ -Brunn-Minkowski 理论的扩展。在本文中，我们为p内平行体的 quermassintegrals 建立（尖锐的）上界和下界。此外，得到了主不等式的等式的充要条件，这些条件刻画了所谓的切体。