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<p>In this work we introduce a family of conformal flows generalizing the classical Yamabe flow. We prove that for a large class of such flows long-time existence holds, and the arguments are in fact simpler than in the classical case. Moreover, we establish convergence for the case of negative scalar curvature and expect a similar statement for the positive and the flat cases as well.</p>

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Generalized Yamabe Flows

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月27日

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  • Jørgen Olsen Lye,
  • Boris Vertman,
  • Mannaim Gennaro Vitti

摘要

In this work we introduce a family of conformal flows generalizing the classical Yamabe flow. We prove that for a large class of such flows long-time existence holds, and the arguments are in fact simpler than in the classical case. Moreover, we establish convergence for the case of negative scalar curvature and expect a similar statement for the positive and the flat cases as well.