Holder estimates for the CR extension problem

Jinyong Yuan, Purdue University

Abstract

Suppose that M is an abstract smoothly bounded orientable CR manifold of dimension $2n-1$ with CR dimension equal to $n-1.$ Suppose that the Levi form has either at least three positive eigenvalues or $n-1$ negative eigenvalues at each point of M. Suppose that the CR structure is in ${\cal C}\sb{s},$ the Holder class of order s for some $s>0.$ Let $r>0.$ If $s=s(r)$ is large enough, then this CR structure can be extended to an integrable almost complex structure on a 2n-dimensional manifold $\Omega$ with boundary so that $M\subset b\Omega$ and the complex structure is in ${\cal C}\sb{r}.$ It follows that if the Levi form at $z\sb0\in M$ has at least three positive and three negative eigenvalues, or the Levi form has $n-1$ positive eigenvalues, then a neighborhood of $z\sb0$ in M can be embedded in $\doubc\sp{n}$ through a ${\cal C}\sb{r}$ embedding.

Degree

Ph.D.

Advisors

Catlin, Purdue University.

Subject Area

Mathematics

COinS