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Volume 39, Issue 1
Busemann-Petty Type Problem for the General $L_p$-Centroid Bodies

Weidong Wang

DOI: 10.4208/ata.OA-2021-0030

Anal. Theory Appl., 39 (2023), pp. 69-82.

Published online: 2023-03

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  • Abstract

Lutwak showed the Busemann-Petty type problem (also called the Shephard type problem) for the centroid bodies. Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the $L_p$-centroid bodies. In this paper, we obtain an affirmation form and two negative forms of the Busemann-Petty type problem for the general $L_p$-centroid bodies.

  • Keywords

$L_p$-centroid body, general $L_p$-centroid body, Busemann-Petty problem, affirmation form, negation form.

  • AMS Subject Headings

52A40, 52A20, 52A39, 52A38

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-39-69, author = {Wang , Weidong}, title = {Busemann-Petty Type Problem for the General $L_p$-Centroid Bodies}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {1}, pages = {69--82}, abstract = {

Lutwak showed the Busemann-Petty type problem (also called the Shephard type problem) for the centroid bodies. Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the $L_p$-centroid bodies. In this paper, we obtain an affirmation form and two negative forms of the Busemann-Petty type problem for the general $L_p$-centroid bodies.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2021-0030}, url = {http://global-sci.org/intro/article_detail/ata/21462.html} }
TY - JOUR T1 - Busemann-Petty Type Problem for the General $L_p$-Centroid Bodies AU - Wang , Weidong JO - Analysis in Theory and Applications VL - 1 SP - 69 EP - 82 PY - 2023 DA - 2023/03 SN - 39 DO - http://doi.org/10.4208/ata.OA-2021-0030 UR - https://global-sci.org/intro/article_detail/ata/21462.html KW - $L_p$-centroid body, general $L_p$-centroid body, Busemann-Petty problem, affirmation form, negation form. AB -

Lutwak showed the Busemann-Petty type problem (also called the Shephard type problem) for the centroid bodies. Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the $L_p$-centroid bodies. In this paper, we obtain an affirmation form and two negative forms of the Busemann-Petty type problem for the general $L_p$-centroid bodies.

Weidong Wang. (2023). Busemann-Petty Type Problem for the General $L_p$-Centroid Bodies. Analysis in Theory and Applications. 39 (1). 69-82. doi:10.4208/ata.OA-2021-0030
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