Jrgens-Calabi-Pogorelov定理的一个推广(英文)

A Generalization of Jrgens-Calabi-Pogorelov theorem

文章证明了方程(其中d0,d1,…,dn是常数)的任何光滑严格凸的定义在整个Rn的解一定是二次多项式,推广了著名的Jrgens-Calabi-Pogorelov定理.

It is shown that any smooth strictly convex global solution on R^n of det（δ^2u/δξiδξj）=exp｜-∞∑i=1 di δu/δξi -d0｜, where d0, d 1,……, dn are constants, must be a quadratic polynomial. This extends a well-known theorem of Jorgens-Calabi-Pogorelov.