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arXiv 2602.075102026-02math.DGmath.AP

在双曲空间中带有负边界参数的Robin拉普拉斯算子的下界估计

Sharp estimates for the Robin Laplacian under a perimeter constraint in hyperbolic space

Daguang Chen, Shan Li

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AI总结：

本文研究了双曲空间中Robin拉普拉斯算子的特征值问题，证明了测地球在特定条件下最大化特征值，并解决了相关开放问题。

摘要：

本文建立了在双曲空间中，对于具有负边界参数的Robin拉普拉斯算子的第一个特征值的下界，该下界以等周缺陷为参数。这表明，测地球在所有此类域中最大化该特征值，从而部分解决了Celentano、Krejčiřík和Lotoreichik在文献[CKL26]中提出的一个开放问题。此外，我们还推导了在双曲空间中，对于具有正边界参数的Robin拉普拉斯算子的第一个特征值的上界。

英文摘要：

In this paper, we establish a quantitative lower bound, expressed in terms of the isoperimetric deficit, for the normalized first eigenvalue deficit of the Robin Laplacian with a negative boundary parameter on bounded horospherically convex domains in hyperbolic space. As a consequence, the geodesic ball maximizes the first Robin eigenvalue within this class, thereby resolving the higher-dimensional counterpart of an open problem posed by Celentano, Krejčiřík and Lotoreichik in \cite{CKL26}. Furthermore, for a positive boundary parameter, we derive a quantitative upper bound for the normalized difference between the first Robin eigenvalue of such a domain and that of the geodesic ball with the same perimeter.

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