七维四元数 Heisenberg 群上的 Sobolev 不等式极值与四元数接触 Yamabe 问题
微分几何
2008-07-30 v3 偏微分方程分析
摘要
给出了七维球面上四元数接触 Yamabe 问题的完全解。明确描述了七维 Heisenberg 群上 Sobolev 不等式的极值，并确定了 Folland-Stein 嵌入定理中的最佳常数。
引用
@article{arxiv.math/0703044,
title = {Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem},
author = {Stefan Ivanov and Ivan Minchev and Dimiter Vassilev},
journal= {arXiv preprint arXiv:math/0703044},
year = {2008}
}
备注
22 pages, LaTeX 2e, 10pt, exposition extended and clarified, typos corrected, final version to appear in the Journal of the European Math. Soc. (JEMS)