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.
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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 -