Pseudo-Hermitian Geometry in 3D

被引:0
作者
Yang, Paul C. [1 ]
机构
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
来源
GEOMETRIC ANALYSIS | 2020年 / 2263卷
关键词
ISOPERIMETRIC INEQUALITY; CR-MANIFOLDS; INVARIANT; OPERATOR; COMPLEX; SURFACES;
D O I
10.1007/978-3-030-53725-8_4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This chapter concerns CR geometry, a research field for which there is an extremely fruitful interaction of different ideas, ranging from Differential Geometry, Partial Differential Equations and Complex Analysis. First, some basic concepts of the subject are introduced, as well as some conformally covariant operators. Then some surprising relations are shown between the embeddability of abstract CR structures, the spectral properties of the Paneitz operator and the attainment of the Yamabe quotient. Finally, some surface theory is treated, in relation to the isoperimetic problem, the prescribed mean curvature problem and to some Willmore-type functionals.
引用
收藏
页码:113 / 144
页数:32
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