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Supported Blow-Up and Prescribed Scalar Curvature on $S^n$
 
Man Chun Leung National University of Singapore, Singapore, Republic of Singapore
Front Cover for Supported Blow-Up and Prescribed Scalar Curvature on $S^n$
Available Formats:
Electronic ISBN: 978-1-4704-0619-6
Product Code: MEMO/213/1002.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $43.80
Front Cover for Supported Blow-Up and Prescribed Scalar Curvature on $S^n$
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  • Front Cover for Supported Blow-Up and Prescribed Scalar Curvature on $S^n$
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Supported Blow-Up and Prescribed Scalar Curvature on $S^n$
Man Chun Leung National University of Singapore, Singapore, Republic of Singapore
Available Formats:
Electronic ISBN:  978-1-4704-0619-6
Product Code:  MEMO/213/1002.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $43.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2132011; 99 pp
    MSC: Primary 35; Secondary 53;

    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.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. The Subcritical Approach
    • 3. Simple, Towering, Aggregated and Clustered Blow-ups
    • 4. Supported and Collapsed Blow-ups
    • 5. Toward Isolated Blow-ups
    • 6. Toward Supported Blow-up for $\Delta \,\tilde K (0) > 0$ – Excluding Simple Blow-up
    • 7. Excluding Collapsed Isolated Blow-up (${\mbox {Hess}}_o\,\tilde K (0)\,$ Positive Definite)
    • 8. Close Up
    • 9. Single Simple Blow-up and the Proof of the Main Theorem
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Volume: 2132011; 99 pp
MSC: Primary 35; Secondary 53;

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.

  • Chapters
  • 1. Introduction
  • 2. The Subcritical Approach
  • 3. Simple, Towering, Aggregated and Clustered Blow-ups
  • 4. Supported and Collapsed Blow-ups
  • 5. Toward Isolated Blow-ups
  • 6. Toward Supported Blow-up for $\Delta \,\tilde K (0) > 0$ – Excluding Simple Blow-up
  • 7. Excluding Collapsed Isolated Blow-up (${\mbox {Hess}}_o\,\tilde K (0)\,$ Positive Definite)
  • 8. Close Up
  • 9. Single Simple Blow-up and the Proof of the Main Theorem
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