凸体的曲率熵log-Minkowski不等式

The log-Minkowski inequality of curvature entropy for convex bodies

本文获得R2中一般凸体的曲率熵log-Minkowski不等式,去掉对称性条件,并建立R2中凸体锥体积测度的唯一性、体积log-Minkowski不等式和曲率熵log-Minkowski不等式三者之间的等价性.

In this paper,we establish the plane log-Minkowski inequality of curvature entropy for general convex bodies without the symmetry assumption.The equivalences of the uniqueness of cone-volume measure,the log-Minkowski inequality of volume,and the log-Minkowski inequality of curvature entropy for general convex bodies inR?areshown.