Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions
Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions
复制标题
DOI：
--
复制
发表时间：
2009-12
期刊：
影响因子：
--
通讯作者：
Szu-yu Sophie Chen
中科院分区：
文献类型：
--
作者：
Szu-yu Sophie Chen
1992年，Escobar在Riemann映射定理的启发下，考虑了n维大于2的带边界流形上的Yamabe问题。问题在于找到一个共形度量，使标量曲率为零，平均曲率是常数的边界上。通过使用局部测试函数构造，我们能够西雅图Escobar和Marques的作品中留下的最多的情况。此外，我们减少了剩余的情况下，正质量定理。在这个证明中，我们使用的方法在以前的作品Brendle和Brendle和作者。
In 1992, motivated by Riemann mapping theorem, Escobar considered a version of Yamabe problem on manifolds of dimension n greater than 2 with boundary. The problem consists in finding a conformal metric such that the scalar curvature is zero and the mean curvature is constant on the boundary. By using a local test function construction, we are able to seattle the most cases left by Escobar's and Marques's works. Moreover, we reduce the remaining case to the positive mass theorem. In this proof, we use the method developed in previous works by Brendle and by Brendle and the author.