We consider a one parameter family of Laplacians on a closed manifold and study the semi-classical limit of its analytically parametrized eigenvalues. Our results establish a vector valued analogue of a theorem for scalar Schrödinger operators on Euclidean space by Luc Hillairet which applies to geometric operators like Witten’s Laplacian on differential forms.

中文翻译：

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半经典极限下的解析本征支。

我们考虑闭流形上的拉普拉斯单参数族，并研究其解析参数化特征值的半经典极限。我们的结果建立了 Luc Hillairet 提出的欧几里得空间上标量薛定谔算子定理的向量值模拟，该定理适用于微分形式上的维滕拉普拉斯算子等几何算子。