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Compactness and non-compactness for the Yamabe problem on manifolds with boundary
Abstract We study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when the boundary is umbilic and the dimension <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>≤</m:mo> <m:mn>24</m:mn> </m:mrow> </m:math> ${n\leq 24}$ . …