Stronger versions of the Orlicz-Petty projection inequality

By K. Boroczky. 2011

67 citations recorded by the source corpus.

We verify a conjecture of Lutwak, Yang, Zhang about the equality case in the Orlicz-Petty projection inequality, and provide an essentially optimal stability version.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/81d74310d0371467a688e8ccdcf2f45411266006

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Deping Ye
2. Richard J. Gardner
3. Wolfgang H. Weil
4. Daniel Hug
5. Van Hoang Nguyen
6. Sudan Xing
7. Baocheng Zhu
8. Yiming Zhao

In Mathematical Physics

1. Richard J. Gardner
2. Wolfgang H. Weil
3. Deping Ye
4. Daniel Hug
5. Van Hoang Nguyen

Citations in the corpus

• New Orlicz affine isoperimetric inequalities (2014, background): “Important contributions include the study of Logarithmic Minkowski and even Orlicz Minkowski problems [7, 15]; the logBrunn-Minkowski-inequality [5]; stronger versions of the Orlicz-Petty projection inequality [6]; Orlicz Busemann-Petty centroid inequality [10, 20, 53] among others.”
• New approach to the affine P\'olya-Szeg\"o principle and the stability version of the affine Sobolev inequality (2015, methodology): “In fact, Wang [61] proved a bit more, namely a stability estimate for the affine Pólya-Szegö principle by using a recent stability result for the Lp Petty projection inequality establisheb by Böröczky [5] and a quantitative Pólya-Szegö pinciple for convex symmetrization [19].”
• The dual Orlicz–Brunn–Minkowski theory ☆ (2014, background): “) The new theory has already attracted considerable interest; see, for example, [2, 3, 4, 5, 21, 22, 25, 26, 39, 40, 41, 46].”