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Supported Blow-Up and Prescribed Scalar Curvature on Sn (Memoirs of the American Mathematical Society)

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Supported Blow-Up and Prescribed Scalar Curvature on Sn (Memoirs of the American Mathematical Society)

Supported Blow-Up and Prescribed Scalar Curvature on Sn (Memoirs of the American Mathematical Society) by Man Chun Leung
English | 2011 | ISBN: 0821853376 | 99 Pages | PDF | 858.24 KB

The author expounds the notion of supported blow-up and applies it to study the renowned Nirenberg/Kazdan-Warner problem on $S^n$. When $n \ge 5$ and under some mild conditions, he shows 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 the author to obtain a general existence theorem for $n \ge 5$ with rather natural condition.