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Abstract
We expound the notion of supported blow-up and apply it to study the renowned Nirenberg/Kazdan-Warner problem on S n. When n ≥ 5 and under some mild conditions, we show that blow-up at a point with positive definite Hessian has to be a supported isolated blow-up, which, when combined with a uniform volume bound, is a removable singularity. A new asymmetric condition is introduced to exclude single simple blow-up. These enable us to obtain a general existence theorem for n ≥ 5 with rather natural condition. © 2011 American Mathematical Society.
Keywords
Blow-up, Noncompactness, Removable singularity, Scalar curvature
Source Title
Memoirs of the American Mathematical Society
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Series/Report No.
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Date
2011-09
DOI
Type
Article