The Yamabe problem for higher order curvatures
微分几何
2007-05-23 v1 偏微分方程分析
摘要
Let M be a compact Riemannian manifold of dimension n. The k-curvature, for k=1,2,..n, is defined as the k-th elementary symmetric polynomial of the eigenvalues of the Schouten tenser. The k-Yamabe problem is to prove the existence of a conformal metric whose k-curvature is a constant. When k=1, it reduces to the well-known Yamabe problem. Under the assumption that the metric is admissible, the existence of solutions to the k-Yamabe problem was recently proved by Gursky and Viaclovsky for k>n/2. In this paper we prove the existence of solutions for the remaining cases k <n/2, k=n/2, assuming that the equation is variational.
引用
@article{arxiv.math/0505463,
title = {The Yamabe problem for higher order curvatures},
author = {Weimin Sheng and Neil S Trudinger and Xu-jia Wang},
journal= {arXiv preprint arXiv:math/0505463},
year = {2007}
}