TITLE

On Harnack inequalities and singularities of admissible metrics in the Yamabe problem

AUTHOR(S)
Trudinger, Neil S.; Xu-Jia Wang
PUB. DATE
July 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Jul2009, Vol. 35 Issue 3, p317
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper we study the local behaviour of admissible metrics in the k-Yamabe problem on compact Riemannian manifolds ( M, g0) of dimension n = 3. For n/2 < k < n, we prove a sharp Harnack inequality for admissible metrics when ( M, g0) is not conformally equivalent to the unit sphere S n and that the set of all such metrics is compact. When ( M, g0) is the unit sphere we prove there is a unique admissible metric with singularity. As a consequence we prove an existence theorem for equations of Yamabe type, thereby recovering as a special case, a recent result of Gursky and Viaclovsky on the solvability of the k-Yamabe problem for k > n/2.
ACCESSION #
36624684

 

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