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arXiv · 1708.04077

Critical Kahler toric metrics for the invariant first eigenvalue

Rosa Sena-Dias
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Abstract

In [LS], it is shown shown that the first eigenvalue of the Laplacian restricted to the space of invariant functions on a toric Kähler manifold (i.e. $λ_1^\mathbb{T}$, the invariant first eigenvalue) is an unbounded function of the toric Kähler metric. In this note we show that, seen as a function on the space of toric Kähler metrics on a fixed toric manifold, $λ_1^\mathbb{T}$ admits no analytic critical points. We also show that on $S^2$, the first eigenvalue of the Laplacian restricted to the space of $S^1$-equivariant functions of any given integer weight admits no critical points.

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Rosa Sena-Dias. 2017-08-14. Critical Kahler toric metrics for the invariant first eigenvalue. https://arxiv.org/abs/1708.04077

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