Compactness and non-compactness for Yamabe-type problems

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The Yamabe equation is one of the most natural and well-studied second-order semilinear elliptic equations arising in geometric variational problems. The existence theory is classical, while it follows from the works (Brendle, J Am Math Soc 21:951–979, 2008; Brendle and Marques, J Differ Geom 81:225–250, 2009) and (Khuri et al., J Differ Geom 81:143–196, 2009) that n = 25 is a critical dimension for compactness/noncompactness issues (or a priori estimates). In this survey article we review these results and discuss more recent related work on Yamabe-type problems.

Original languageEnglish (US)
Pages (from-to)121-131
Number of pages11
JournalProgress in Nonlinear Differential Equations and Their Application
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mechanics
  • Mathematical Physics
  • Control and Optimization
  • Applied Mathematics


  • Covariance
  • Manifold


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