The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy- Kuhota for...The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy- Kuhota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.展开更多
A class of geometric quantities for convex bodies is introduced iu the framework of Orlicz Brunn- Minkowski theory. It is shown that these new geometric quantities are affine invariant and precisely the generalization...A class of geometric quantities for convex bodies is introduced iu the framework of Orlicz Brunn- Minkowski theory. It is shown that these new geometric quantities are affine invariant and precisely the generalizations of classical affine quermassintegrals.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11001163)Innovation Program of Shanghai Municipal Education Commission(Grant No.11YZ11)
文摘The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy- Kuhota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.
基金supported by National Natural Science Foundation of China(Grant No.11471206)
文摘A class of geometric quantities for convex bodies is introduced iu the framework of Orlicz Brunn- Minkowski theory. It is shown that these new geometric quantities are affine invariant and precisely the generalizations of classical affine quermassintegrals.
