Maximizing the first eigenvalue of the Jacobi operator

2020/01/09 by Montenegro, J. Fabio, Vieira, F. Damiana
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.03137

Abstract

We consider the Jacobi operator, defined on a closed oriented hypersurfaces immersed in the Euclidean space with the same volume of the unit sphere. We show a local generalization for the classical result of the Willmore functional for the Euclidean sphere. As a consequence, we prove that the first eigenvalue of the Jacobi operator in the Euclidean sphere is a local maximum and this result is a global one in the closed oriented surfaces space of ℝ³ and genus zero.

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