General Measure Extensions of Projection Bodies
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916773193842688 |
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| author | Langharst, Dylan Roysdon, Michael Zvavitch, Artem |
| author_facet | Langharst, Dylan Roysdon, Michael Zvavitch, Artem |
| contents | The inequalities of Petty and Zhang are affine isoperimetric-type inequalities providing sharp bounds for $\text{vol}^{n-1}_{n}(K)\text{vol}_n(Π^\circ K),$ where $ΠK$ is a projection body of a convex body $K$. In this paper, we present a number of generalizations of Zhang's inequality to the setting of arbitrary measures. In addition, we introduce extensions of the projection body operator $Π$ to the setting of arbitrary measures and functions, while providing associated inequalities for this operator; in particular, Zhang-type inequalities. Throughout, we apply shown results to the standard Gaussian measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_13212 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | General Measure Extensions of Projection Bodies Langharst, Dylan Roysdon, Michael Zvavitch, Artem Functional Analysis Differential Geometry Metric Geometry Primary: 52A39, 52A40, Secondary: 28A75 The inequalities of Petty and Zhang are affine isoperimetric-type inequalities providing sharp bounds for $\text{vol}^{n-1}_{n}(K)\text{vol}_n(Π^\circ K),$ where $ΠK$ is a projection body of a convex body $K$. In this paper, we present a number of generalizations of Zhang's inequality to the setting of arbitrary measures. In addition, we introduce extensions of the projection body operator $Π$ to the setting of arbitrary measures and functions, while providing associated inequalities for this operator; in particular, Zhang-type inequalities. Throughout, we apply shown results to the standard Gaussian measure. |
| title | General Measure Extensions of Projection Bodies |
| topic | Functional Analysis Differential Geometry Metric Geometry Primary: 52A39, 52A40, Secondary: 28A75 |
| url | https://arxiv.org/abs/2106.13212 |