Conformal scalar curvature equation on S^n: functions with two close critical points (twin pseudo-peaks)
Analysis of PDEs
2017-01-24 v1
Abstract
By using the Lyapunov-Schmidt reduction method without perturbation, we consider existence results for the conformal scalar curvature on S^n (n greater or equal to 3) when the prescribed function (after being projected to R^n) has two close critical points, which have the same value (positive), equal "flatness" (twin, flatness < n - 2), and exhibit maximal behavior in certain directions (pseudo-peaks). The proof relies on a balance between the two main contributions to the reduced functional - one from the critical points and the other from the interaction of the two bubbles.
Keywords
Cite
@article{arxiv.1701.06277,
title = {Conformal scalar curvature equation on S^n: functions with two close critical points (twin pseudo-peaks)},
author = {Man Chun Leung and Feng Zhou},
journal= {arXiv preprint arXiv:1701.06277},
year = {2017}
}
Comments
Appendix included