Supported blow-up and prescribed scalar curvature on Sn / Man Chun Leung.

Format:

Book

Author/Creator:

Leung, Man Chun, 1963- author.

Series:

Memoirs of the American Mathematical Society ; Volume 213, Number 1002.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 213, Number 1002

Language:

English

Subjects (All):

Blowing up (Algebraic geometry).

Curvature.

Transformations (Mathematics).

Differential equations, Elliptic.

Physical Description:

1 online resource (99 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2011.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. The Subcritical Approach""; ""Chapter 3. Simple, Towering, Aggregated and Clustered Blow-ups""; ""Chapter 4. Supported and Collapsed Blow-ups""; ""Chapter 5. Toward Isolated Blow-ups""; ""Chapter 6. Toward Supported Blow-up for (0) > 0 � Excluding Simple Blow-up""; ""Chapter 7. Excluding Collapsed Isolated Blow-up (Hesso (0) Positive Definite)""; ""Chapter 8. Close Up""; ""Chapter 9. Single Simple Blow-up and the Proof of the Main Theorem""; ""Bibliography""

Notes:

"Volume 213, Number 1002 (third of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0619-5