Abstract
The cigar soliton is called Euclidean-Witten black hole under first-order Ricci flow of the world-sheet sigma model in physics. Thus, cigar soliton is of great significance in both geometry and physics. In addition, in order to describe vibrations of a clamped plate in elastic mechanics, one must consider an eigenvalue problem with fixed boundary condition for bi-harmonic operator, called a clamped plate problem. As a generalization, we consider the eigenvalue problem with Dirichlet boundary condition for the bi-drifting Laplacian and obtain two eigenvalue inequalities of the bi-drifting Laplacian on the bounded domains of cigar soliton in this paper.
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