On the prescribed scalar curvature problem in RN, local uniqueness and periodicity
Journal
Journal des Mathematiques Pures et Appliquees
Date Issued
2014
Author(s)
Abstract
We obtain a local uniqueness result for bubbling solutions of the prescribed scalar curvature problem in RN. Such a result implies that some bubbling solutions preserve the symmetry from the scalar curvature K(y). In particular, we prove in this paper that if K(y) is periodic in y1 with period 1 and has a local maximum at 0, then a bubbling solution whose blow-up set is {(jL, 0, ..., 0):j=0, ±1, ±2, ...} must be periodic in y1 provided the positive integer L is large enough.
Type
journal article