完备α度量的相对抛物型仿射球(英文)

Relative Parabolic Affine Hyperspheres With Complete a-metric

摘要:设y:M→R^(n+1)是一个光滑连通流形到实仿射空间R^(n+1)的局部强凸浸入超曲面,而且是一个定义在区域Ω(?)R^n上的严格凸函数x_(n+1)=f(x_1,x_2,…,x_n)的图.在α相对法化下,相对抛物型仿射球满足一个四阶非线性偏微分方程组.本文证明了这类抛物型仿射球的一个新的Bernstein性质.

Let y ： M → Rn＋1 be a locally strongly convex hypersurface immersion of a smooth, connected manifold into the real affine space Rn＋1, given as the graph of a strictly convex function x n＋1 = f（x1,x2…,xn） defined on a domain Ω C Rn. With the s-relative normalization, the relative parabolic affine hyperspheres satisfy a system of fourth order non- linear partial differential equations. In this paper we prove a new Bernstein property of these relative parabolic affine hyperspheres.