Supported Blow-Up and Prescribed Scalar Curvature on $S^n$

Released on by Man Chun Leung
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  • Supported Blow-Up and Prescribed Scalar Curvature on $S^n$ Book Detail

  • Author : Man Chun Leung
  • Release Date : 2011
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 112
  • ISBN 13 : 0821853376
  • File Size : 11,11 MB
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Supported Blow-Up and Prescribed Scalar Curvature on $S^n$ by Man Chun Leung PDF Summary

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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