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Dragomir, Sorin

Minimality in CR geometry and the CR Yamabe problem on CR manifolds with boundary. (English) Zbl 1148.53042

J. Math. Soc. Japan 60, No. 2, 363-396 (2008).
The author formulates the CR Yamabe problem as the Yamabe problem for the Fefferman metric, which is reduced to finding a positive function as the solution of a nonlinear subelliptic problem of variational origin. The boundary condition of this problem turned out to be the problem of minimality of boundary in the canonical circle bundle. This condition projected on manifold is interpreted as CR Yamabe problem. In the paper, only geometric aspects are discussed.
Reviewer: Vyacheslav S. Kalnitsky (St. Peterburg)

Cited in 1 Document

MSC:

53C40 Global submanifolds
32V20 Analysis on CR manifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)

Keywords:

CR manifold; minimal submanifold; Fefferman metric; CR Yamabe problem
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\textit{S. Dragomir}, J. Math. Soc. Japan 60, No. 2, 363--396 (2008; Zbl 1148.53042)
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