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In this chapter, we first provide evolution formulas for the eigenvalue of some cooperative \((p,q)\) -biharmonic system on Riemannian manifolds under the (unnormalized) Ricci flow and normalized Ricci flow. Then, we provide some monotonic quantities under this flow. Moreover, as an application of the evolution equation, we give an example.

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The Principal Eigenvalue of a \((p,q)\) -Biharmonic System Along the Ricci Flow

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  • 发表日期：

    2026年

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  • Shahroud Azami,
  • Gh. Fasihi-Ramandi

摘要

In this chapter, we first provide evolution formulas for the eigenvalue of some cooperative \((p,q)\) -biharmonic system on Riemannian manifolds under the (unnormalized) Ricci flow and normalized Ricci flow. Then, we provide some monotonic quantities under this flow. Moreover, as an application of the evolution equation, we give an example.