Compactness and non-compactness for the Yamabe problem on manifolds with boundary
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چکیده
منابع مشابه
Compactness and Non-compactness for the Yamabe Problem on Manifolds with Boundary
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 n ≤ 24. The Weyl Vanishing Theorem is also established under these hypotheses, and we provide counter-examples to compactness when n ≥ 25. Lastly, our methods...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2017
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2014-0083