A sharp inequality for trace-free matrices with applications to hypersurfaces

Case, Jeffrey; Tyrrell, Aaron

doi:10.1090/proc/16657

A sharp inequality for trace-free matrices with applications to hypersurfaces
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by Jeffrey S. Case and Aaron J. Tyrrell;

Proc. Amer. Math. Soc. 152 (2024), 823-828

DOI: https://doi.org/10.1090/proc/16657

Published electronically: November 21, 2023

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Abstract:

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.

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