We investigate the geometric properties of Steklov eigenfunctions in smooth manifolds. We derive the refined doubling estimates and Bernstein’s inequalities. For the real analytic manifolds, we are able to obtain the sharp upper bound for the measure of interior nodal sets.

中文翻译：

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Steklov特征函数的几何和内部节点集

我们研究了光滑流形中Steklov特征函数的几何性质。我们得出精确的加倍估计和伯恩斯坦不等式。对于真实的分析流形，我们能够获得用于测量内部节点集的尖锐上限。