A SHARP INEQUALITY FOR TRACE-FREE MATRICES WITH APPLICATIONS TO HYPERSURFACES
We derive a sharp inequality relating the second and fourth elementary symmetric functions of the eigenvalues of a trace-free matrix and give two applications. First, we give a new proof of the classification of conformally flat hypersurfaces in spaceforms. Second, we construct a functional which characterizes rotational hypersurfaces and catenoids.
First published in Proceedings of the American Mathematical Society on 2023-11-21, published by the American Mathematical Society. © 2023 American Mathematical Society.
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Work Title | A SHARP INEQUALITY FOR TRACE-FREE MATRICES WITH APPLICATIONS TO HYPERSURFACES |
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License | CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives) |
Work Type | Article |
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Publication Date | November 21, 2023 |
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Deposited | November 16, 2024 |
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