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On the Minkowski deficit for surfaces of revolution
Abstract
By studying the classical Minkowski's inequality, 4πA≤ M2, relating area and mean curvature, in the particular case of convex surfaces of revolution, one is led to a functional inequality that holds for general functions. We state and prove this inequality obtaining a new proof of Minkowski's inequality in this particular case and we establish a sharp inequality between the Minkowski deficit of the surface and the isoperimetric deficit of any meridian curve.
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BibTeX
@misc{bruna2026minkowski,
title = {{On the Minkowski deficit for surfaces of revolution}},
author = {Joaquim Bruna and Julià Cufí and Agustí Reventós},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16792},
eprint = {2609.16792},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16792},
}
RIS
TY - UNPB
TI - On the Minkowski deficit for surfaces of revolution
AU - Joaquim Bruna
AU - Julià Cufí
AU - Agustí Reventós
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16792
UR - https://arxiv.org/abs/2609.16792
AB - By studying the classical Minkowski's inequality, 4πA≤ M^2, relating area and mean curvature, in the particular case of convex surfaces of revolution, one is led to a functional inequality that holds for general functions. We state and prove this inequality obtaining a new proof of Minkowski's inequality in this particular case and we establish a sharp inequality between the Minkowski deficit of the surface and the isoperimetric deficit of any meridian curve.
ER -