Spectral Bounds for the FirstSteklov  Eigenvalue via Reilly-Type Inequalities

Prepared by   

Muntasir Suhail
Department of Mathematics
College of Science
Qassim University,Buraydah 51452, Saudi Arabia
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Keywords : Steklov eigenvalue ; Reilly inequality ; Spectral theory ; Variational methods ; Riemannian manifolds ; Steklov problem ; Euclidean space.

Abstract.
   In this paper, we present some results regarding Reilly's inequality for the first Steklov eigenvalue. Consider a compact submanifold  with boundary . We will address the Steklov problem, specifically when  represents the length of .