TY - CHAP

T1 - Pseudo-Hermitian Geometry in 3D

AU - Yang, Paul C.

N1 - Publisher Copyright:
© 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85090338715&partnerID=8YFLogxK

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U2 - 10.1007/978-3-030-53725-8_4

DO - 10.1007/978-3-030-53725-8_4

M3 - Chapter

AN - SCOPUS:85090338715

T3 - Lecture Notes in Mathematics

SP - 113

EP - 144

BT - Lecture Notes in Mathematics

PB - Springer

ER -