Isoperimetric inequalities for the mean width of a convex body
โ Scribed by G. D. Chakerian
- Publisher
- Springer
- Year
- 1973
- Tongue
- English
- Weight
- 291 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We prove several isoperimetric inequalities involving the kinetic energy of constant-vorticity #ows through channels of uniform width.
Let g be a smooth function on R n with values in [0, 1]. Using the isoperimetric property of the Gaussian measure, it is proved that ,(8 &1 (Eg))&E,(8 &1 ( g)) E |{g|. Conversely, this inequality implies the isoperimetric property of the Gaussian measure.
Studying first the Euclidean subcase, we show that the Minkowskian width function of a convex body in an n-dimensional (normed linear or) Minkowski space satisfies a specified Lipschitz condition.