| eBook 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 |
| eBook 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 213; 2011; 99 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. The Subcritical Approach
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3. Simple, Towering, Aggregated and Clustered Blow-ups
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4. Supported and Collapsed Blow-ups
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5. Toward Isolated Blow-ups
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6. Toward Supported Blow-up for $\Delta \,\tilde K (0) > 0$ – Excluding Simple Blow-up
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7. Excluding Collapsed Isolated Blow-up (${\mbox {Hess}}_o\,\tilde K (0)\,$ Positive Definite)
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8. Close Up
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9. Single Simple Blow-up and the Proof of the Main Theorem
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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
