凸区域上的p-阶特征函数及相关的度量（英文）

The p-th Characteristic Function and Associated Metric on a Convex Domain

考虑强凸有界区域上的p-阶特征函数,本文给出了它对一类Monge-Ampère方程解的渐近展开式,另一方面考虑由p-阶特征函数定义的一个黎曼度量,证明了它的截面曲率在边界上趋于-1,且它的曲率张量及各阶共变微分的范数是有界的.

Considering the p-th characteristic function on a strongly convex bounded domain Ω, we give its asymptotic expansion with respect to the solution of Monge-Ampère equation. On the other hand, considering a Riemannian metric defined by the p-th characteristic function, we show that its sectional curvatures tend to -1 on the boundary δΩ, and the norms of its curvature tensors and of all their covariant derivatives are bounded.