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Volume 31, Issue 4
$L_p$-Centroid Bodies and Its Characterizations

Tongyi Ma & Deyan Zhang

DOI: 10.13447/j.1674-5647.2015.04.05

Commun. Math. Res., 31 (2015), pp. 333-344.

Published online: 2021-05

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  • Abstract

In this paper, we study the characteristic properties for $L_p$-centroid bodies, and an improved version of Busemann-Petty problem for $L_p$-centroid bodies is obtained. In addition, using the definitions of $L_p$-pole curvature image and $L_p$-affine surface area, a new proof of Busemann-Petty problem for $L_p$-centroid bodies is given.

  • Keywords

convex body, star body, centroid body, $L_p$-centroid body, Busemann-Petty problem.

  • AMS Subject Headings

52A40, 52A20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-333, author = {Ma , Tongyi and Zhang , Deyan}, title = {$L_p$-Centroid Bodies and Its Characterizations}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {4}, pages = {333--344}, abstract = {

In this paper, we study the characteristic properties for $L_p$-centroid bodies, and an improved version of Busemann-Petty problem for $L_p$-centroid bodies is obtained. In addition, using the definitions of $L_p$-pole curvature image and $L_p$-affine surface area, a new proof of Busemann-Petty problem for $L_p$-centroid bodies is given.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.05}, url = {http://global-sci.org/intro/article_detail/cmr/18914.html} }
TY - JOUR T1 - $L_p$-Centroid Bodies and Its Characterizations AU - Ma , Tongyi AU - Zhang , Deyan JO - Communications in Mathematical Research VL - 4 SP - 333 EP - 344 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.04.05 UR - https://global-sci.org/intro/article_detail/cmr/18914.html KW - convex body, star body, centroid body, $L_p$-centroid body, Busemann-Petty problem. AB -

In this paper, we study the characteristic properties for $L_p$-centroid bodies, and an improved version of Busemann-Petty problem for $L_p$-centroid bodies is obtained. In addition, using the definitions of $L_p$-pole curvature image and $L_p$-affine surface area, a new proof of Busemann-Petty problem for $L_p$-centroid bodies is given.

Tongyi Ma & Deyan Zhang. (2021). $L_p$-Centroid Bodies and Its Characterizations. Communications in Mathematical Research . 31 (4). 333-344. doi:10.13447/j.1674-5647.2015.04.05
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