Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions
Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions
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DOI：
10.1007/s002080050246
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发表时间：
1998-12
影响因子：
1.4
通讯作者：
B. Berndtsson
中科院分区：
文献类型：
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作者：
B. Berndtsson
若R_n（x，y）是Rn x× Rm y中的凸函数，则R_n（x）= inf y R_n（x，y）的所谓边际函数也是凸的。这一事实，称为凸函数的最小值原理，是几何学上显而易见的事实的解析对应物，即凸集的投影是凸的。(To看到这个，注意{（x，t）;（x）< t}= πx {（x，y，t）;（x，y）< t}。
If ϕ (x, y) is a convex function in Rn x× Rm y, then the so called marginal function of ϕ ϕ∗(x)= inf y ϕ (x, y) is again convex. This fact, known as the minimum principle for convex functions, is the analytic counterpart of the geometrically obvious fact that the projections of convex sets are convex.(To see this, note that {(x, t); ϕ∗(x)< t}= πx {(x, y, t); ϕ (x, y)< t}.)