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Rigidity of a trace estimate for Steklov eigenvalues
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-01-11 , DOI: 10.1016/j.jde.2020.12.036 Yongjie Shi , Chengjie Yu
中文翻译:
Steklov特征值的痕量估计值的刚性
更新日期:2021-01-12
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-01-11 , DOI: 10.1016/j.jde.2020.12.036 Yongjie Shi , Chengjie Yu
In this short note, we show the rigidity of a trace estimate for Steklov eigenvalues with respect to functions in our previous work (Shi and Yu (2016) [13]). Namely, we show that equality of the estimate holds if and only if the manifold is a direct product of a round ball and a closed manifold. The key ingredient in the proof is a splitting theorem for flat and totally geodesic Riemannian submersions which may be of independent interests.
中文翻译:
Steklov特征值的痕量估计值的刚性
在这篇简短的笔记中,我们展示了Steklov特征值的痕迹估计相对于我们先前工作中的函数的刚性(Shi and Yu(2016)[13])。即,我们证明,当且仅当流形是圆球和闭合流形的直接乘积时,估计的等价性成立。证明中的关键要素是平分和完全测地的黎曼浸没式的分裂定理,这可能是有独立利益的。