A classification of \({\text {SL}}(n)\) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as \({\text {SL}}(n)\) and translation invariant valuations on log-concave functions.

中文翻译：

---

对数凹凹函数的估值

建立了\（{\ text {SL}}（n）\）的分类和对数凹函数的平移协变量Minkowski估值。对矩矢量和最近引入的对数凹函数的水平集进行了表征。此外，欧拉特征和体积的类似物的特征是\（{\ text {SL}}（n）\），并且具有对数凹函数的平移不变估值。