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Research Article | Open Access

The L p -Petty projection inequality for s-concave functions

Tian Gao, Dan Ma( )
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
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Abstract

We study the "functionalization" of the L p -projection body and two related important inequalities in geometry. On the class of s-concave functions, a general function counterpart of the L p -projection body is introduced. In addition, the L p -Petty projection inequality and the L p isoperimetric inequality are established on this class. Finally, we show that the L p -Petty projection inequality strengthens the L p isoperimetric inequality on the same class.

Keywords

s-concave functionLp-projection bodyLp-Petty projection inequalityLp isoperimetric inequality
CLC number: 26D10, 52A40

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 7706-7716
DOI: 10.3934/math.2025353

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Cite this article:
Gao T, Ma D. The L p -Petty projection inequality for s-concave functions. AIMS Mathematics, 2025, 10(4): 7706-7716. https://doi.org/10.3934/math.2025353

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Received: 06 January 2025
Revised: 24 March 2025
Accepted: 26 March 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)