A Lichnerowicz-type estimate for Steklov eigenvalues on graphs and its rigidity
Yongjie Shi, Chengjie Yu
TL;DR
This paper establishes a Lichnerowicz-type lower bound for the first Steklov eigenvalues on graphs and explores conditions under which this bound is attained, highlighting rigidity phenomena.
Contribution
It introduces a novel estimate for Steklov eigenvalues on graphs and analyzes the rigidity conditions for equality.
Findings
Derived a lower bound for Steklov eigenvalues on graphs
Identified conditions for rigidity when the bound is achieved
Extended classical estimates to the graph setting
Abstract
In this paper, we obtain a Lichnerowicz-type estimate for the first Steklov eigenvalues on graphs and discuss its rigidity.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · advanced mathematical theories · Numerical methods in inverse problems