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Volume 32, Issue 3
Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bodies

Yao Dan & Qi Guo

Commun. Math. Res., 32 (2016), pp. 207-216.

Published online: 2021-05

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  • Abstract

We introduce a family of measures (functions) of asymmetry for convex bodies and discuss their properties. It turns out that this family of measures shares many nice properties with the mean Minkowski measures. As the mean Minkowski measures describe the symmetry of lower dimensional sections of a convex body, these new measures describe the symmetry of lower dimensional orthogonal projections.

  • Keywords

mean Minkowski measure, asymmetry, symmetry, simplex.

  • AMS Subject Headings

52A20, 52A38, 52A39, 52A40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-207, author = {Yao and Dan and and 18534 and and Yao Dan and Qi and Guo and and 18535 and and Qi Guo}, title = {Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bodies}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {3}, pages = {207--216}, abstract = {

We introduce a family of measures (functions) of asymmetry for convex bodies and discuss their properties. It turns out that this family of measures shares many nice properties with the mean Minkowski measures. As the mean Minkowski measures describe the symmetry of lower dimensional sections of a convex body, these new measures describe the symmetry of lower dimensional orthogonal projections.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.03.03}, url = {http://global-sci.org/intro/article_detail/cmr/18892.html} }
TY - JOUR T1 - Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bodies AU - Dan , Yao AU - Guo , Qi JO - Communications in Mathematical Research VL - 3 SP - 207 EP - 216 PY - 2021 DA - 2021/05 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.03.03 UR - https://global-sci.org/intro/article_detail/cmr/18892.html KW - mean Minkowski measure, asymmetry, symmetry, simplex. AB -

We introduce a family of measures (functions) of asymmetry for convex bodies and discuss their properties. It turns out that this family of measures shares many nice properties with the mean Minkowski measures. As the mean Minkowski measures describe the symmetry of lower dimensional sections of a convex body, these new measures describe the symmetry of lower dimensional orthogonal projections.

Dan Yao & Qi Guo. (2021). Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bodies. Communications in Mathematical Research . 32 (3). 207-216. doi:10.13447/j.1674-5647.2016.03.03
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