平面三角形的径向平均体

The radial mean bodies of triangles in the plane

主要研究了平面三角形的径向平均体,得到了平面三角形的任意阶径向平均体为原点对称的六边形,且给出径向平均体不具有单调性的精确反例,并通过研究三角形的p阶径向平均体面积的单调性,得到平面三角形的John椭球与其p阶径向平均体之间的包含关系。

The radial mean bodies of triangles in the plane are discussed and found that they are hexagons with symmetric origin.An example can be provided to prove the radial mean bodies have not the monotonicity.Then,the relation of inclusion between radial mean bodies and John ellipsoid are obtained.