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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Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-5337-5 (9780821853375)
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Schweitzer Klassifikation
Man Chun Leung is at National University of Singapore, Republic of Singapore