论文标题
关于平行物体的等值仪的单调性
On the monotonicity of the isoperimetric quotient for parallel bodies
论文作者
论文摘要
凸体的整个内部和外部平行物体家族的等等视商在平行物体的定义参数中降低，以及那些凸体的表征，该凸体的表征在其域内的某个间隔上恰好是恒定的。这是相对于任意规体的，将经典的欧几里得设置为特定情况。对于与平行物体密切相关的乌尔夫形状家族的不同家族也建立了类似的结果。这些引起了等等型问题的解决方案。此外，还获得了与表面积和体积不同的其他QuermassIntegrals的单调性的新结果，用于平行物体的家族。
The isoperimetric quotient of the whole family of inner and outer parallel bodies of a convex body is shown to be decreasing in the parameter of definition of parallel bodies, along with a characterization of those convex bodies for which that quotient happens to be constant on some interval within its domain. This is obtained relative to arbitrary gauge bodies, having the classical Euclidean setting as a particular case. Similar results are established for different families of Wulff shapes that are closely related to parallel bodies. These give rise to solutions of isoperimetric-type problems. Furthermore, new results on the monotonicity of quotients of other quermassintegrals different from surface area and volume, for the family of parallel bodies, are obtained.
