亏格二曲面上第一非平凡特征值的最大化
微分几何
2014-08-12 v2 谱理论
摘要
Laplace 算子的第一非平凡特征值可视为固定曲面上所有单位体积 Riemann 度量空间上的泛函。本文证明了对于亏格为 2 的曲面，该泛函的上确界等于 。这为 Jakobson、Levitin、Nadirashvili、Nigam 和 Polterovich 提出的猜想提供了肯定的回答。
引用
@article{arxiv.1309.5057,
title = {Maximization of the first nontrivial eigenvalue on the surface of genus two},
author = {Mikhail A. Karpukhin},
journal= {arXiv preprint arXiv:1309.5057},
year = {2014}
}
备注
This paper has been withdrawn by the author due to a crucial mistake in the equality $\sigma^2 = id$, which should be $\sigma^2 = T$