Supported Blow-Up and Prescribed Scalar Curvature on Sn

(Memoirs of the American Mathematical Society)

5bdcec0ea1cd3.jpg Author Man Chun Leung
Isbn 9780821853375
File size 858.24KB
Year 2011
Pages 99
Language English
File format PDF
Category Mathematics

Book Description:

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.



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