The sharp estimates for the first eigenvalue of Paneitz operator on 4-dimensional submanifolds

2010/10/15 by Daguang Chen, Haizhong Li, Chen, Daguang +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.DG

paper · pdf · doi:10.48550/arxiv.1010.3102

arxiv created 2010/10/15 · openalex publication_date 2010/10/15 · arxiv updated 2010/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we obtain the sharp estimates for the first eigenvalue of Paneitz operator for 4-dimensional compact submanifolds in Euclidean space. Since unit spheres and projective spaces can be canonically imbedded into Euclidean space, the corresponding estimates for the first eigenvalue are also obtained.

Citations

• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces

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