Yamabe Flow on Non-compact Manifolds with Unbounded Initial Curvature

  • Mario B. SchulzEmail author


We prove global existence of Yamabe flows on non-compact manifolds M of dimension \(m\ge 3\) under the assumption that the initial metric \(g_0=u_0g_M\) is conformally equivalent to a complete background metric \(g_M\) of bounded, non-positive scalar curvature and positive Yamabe invariant with conformal factor \(u_0\) bounded from above and below. We do not require initial curvature bounds. In particular, the scalar curvature of \((M,g_0)\) can be unbounded from above and below without growth condition.


Yamabe flow Non-compact Unbounded scalar curvature Global existence 

Mathematics Subject Classification

53C44 35K55 35A01 



This research was supported by the Swiss National Science Foundation under Grant 200020_159925.


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Authors and Affiliations

  1. 1.ETH ZürichZürichSwitzerland

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