On the Sobolev quotient of three-dimensional CR manifolds

被引：4
|
作者：
Cheng, Jih-Hsin [1 ,2 ]
Malchiodi, Andrea [3 ]
Yang, Paul [4 ]
机构：
[1] Acad Sinica, Inst Math, 6F,Astron Math Bldg 1,Sec 4,Roosevelt Rd, Taipei 10617, Taiwan
[2] NCTS, 6F,Astron Math Bldg 1,Sec 4,Roosevelt Rd, Taipei 10617, Taiwan
[3] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-50126 Pisa, Italy
[4] Princeton Univ, Dept Math, Fine Hall,Washington Rd, Princeton, NJ 08544 USA
来源：
REVISTA MATEMATICA IBEROAMERICANA | 2023年 / 39卷 / 06期
关键词：
CR manifold; Rossi sphere; pseudo-hermitian mass; CR-Sobolev quotient; PANEITZ OPERATOR; YAMABE PROBLEM; CONJECTURE; PROOF;
D O I：
10.4171/RMI/1412
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We exhibit examples of compact three-dimensional CR manifolds of pos-itive Webster class, Rossi spheres, for which the pseudo-hermitian mass, as defined by Cheng-Malchiodi-Yang (2017), is negative, and for which the infimum of the CR-Sobolev quotient is not attained. To our knowledge, this is the first geometric context on smooth closed manifolds where this phenomenon arises, in striking con-trast to the Riemannian case.
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页码：2017 / 2066
页数：50
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