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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Open Access
Creators
  1. Jeffrey S. Case
  2. Aaron J. Tyrrell
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
Publisher
  1. Proceedings of the American Mathematical Society
Publication Date November 21, 2023
Publisher Identifier (DOI)
  1. https://doi.org/10.1090/proc/16657
Deposited November 16, 2024

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  • Added case_tyrrell2024-1.pdf
  • Added Creator Jeffrey S. Case
  • Added Creator Aaron J. Tyrrell
  • Published
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