A family of compact strictly pseudoconvex hypersurfaces in C-2 without umbilical points

作者：Ebenfelt Peter^*; Duong Ngoc Son; Zaitsev Dmitri

来源：Mathematical Research Letters, 2018, 25(1): 75-84.

DOI：10.4310/MRL.2018.v25.n1.a4

We prove the following: For epsilon > 0(;) let D-epsilon be the bounded strictly pseudoconvex domain in C-2 given by
(log|z|)(2) + (log|w|)(2) < epsilon(2).
The boundary M-e := dagger D-epsilon C C-2 is a compact strictly pseudoconvex CR manifold without umbilical points. This resolves a long-standing question in complex analysis that goes back to the work of S.-S. Chern and J. K. Moser in 1974.

• 出版日期2018