Abstract We give a new integral formula for the centro-projective area of a convex body, which was first defined by Berck–Bernig–Vernicos. We then use the formula to prove that it is bounded from above by the centro-projective area of an ellipsoid and that equality occurs if and only if the convex set is an ellipsoid.

中文翻译：

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中心投影不等式

摘要 我们给出了一个新的凸体中心投影面积的积分公式，它是由 Berck-Bernig-Vernicos 首次定义的。然后我们使用公式来证明它由椭圆体的中心投影面积从上方有界，并且当且仅当凸集是椭圆体时才会发生等式。