Pseudo-Hermitian Geometry in 3D

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer
Pages113-144
Number of pages32
DOIs
StatePublished - 2020

Publication series

NameLecture Notes in Mathematics
Volume2263
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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  • Cite this

    Yang, P. C. (2020). Pseudo-Hermitian Geometry in 3D. In Lecture Notes in Mathematics (pp. 113-144). (Lecture Notes in Mathematics; Vol. 2263). Springer. https://doi.org/10.1007/978-3-030-53725-8_4