Infinite-time incompleteness of noncompact Yamabe flow

2021/11/05 by Jin Takahashi, Takahashi, Jin, Hikaru Yamamoto +1 · 1 citation
Computer Science · Mathematics · #35A21 #53C18 (Secondary) #53E99 (Primary) 35K67 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2111.03222

openalex publication_date 2021/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the noninheritance of the completeness of the noncompact Yamabe flow. Our main theorem states the existence of a long time solution which is complete for each time and converges to an incomplete Riemannian metric. This shows the occurrence of the infinite-time incompleteness.

Citations

• The yamabe flow on locally conformally flat manifolds with positive ricci curvature
• The Yamabe flow on asymptotically flat manifolds

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• Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation

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