标题： 特征值控制对于Finsler-Laplace算子 显示英文标题

标题： Eigenvalues control for a Finsler--Laplace operator

摘要： 使用第一作者给出的Finsler-Laplacian定义，我们证明了两个双利普希茨Finsler度量具有受控谱。 我们由此推导出几个黎曼结果的推广。 特别是，我们证明了Finsler曲面上的谱由依赖于曲面拓扑和度量的准可逆常数的常数所控制。 与黎曼几何不同，我们随后给出了曲面上具有任意大的第一特征值的高度不可逆度量的例子。 显示英文摘要

摘要： Using the definition of a Finsler--Laplacian given by the first author, we show that two bi-Lipschitz Finsler metrics have a controlled spectrum. We deduce from that several generalizations of Riemannian results. In particular, we show that the spectrum on Finsler surfaces is controlled above by a constant depending on the topology of the surface and on the quasireversibility constant of the metric. In contrast to Riemannian geometry, we then give examples of highly non-reversible metrics on surfaces with arbitrarily large first eigenvalue.