A family of compact strictly pseudoconvex hypersurfaces in $\mathbb{C}^2$ without umbilical points

On the Winding of Pseudoconvex Hypersurfaces along Compact Complex Varieties

Sobolev Space Projections in Strictly Pseudoconvex Domains

The orthogonal projection from a Sobolev space WS(Q) onto the subspace of holomorphic functions is studied. This analogue of the Bergman projection is shown to satisfy regularity estimates in higher Sobolev norms when ß is a smooth bounded strictly pseudoconvex domain in C". The Bergman projection P0: L2(ü) -» L2(S2) n {holomorphic functions}, where S2 c C" is a smooth bounded domain, has prove...

Scattering Theory for Strictly Pseudoconvex Domains

The spectral theory of a metric of Bergman type on a strictly pseudoconvex manifold is described and the scattering matrix is shown to be a pseudodifferential operator of Heisenberg type.

Poisson geometry and deformation quantization near a strictly pseudoconvex boundary

Let X be a complex manifold with strongly pseudoconvex boundary M . If ψ is a defining function for M , then − logψ is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form σ = i∂∂(− logψ) is a symplectic structure on the complement of M in a neighborhood in X of M ; it blows up along M . The Poisson structure obtained by inverting σ extends smoothly across M and determines a cont...

Umbilical hypersurfaces of Minkowski spaces

In this paper, by the Gauss equation of the induced Chern connection for Finsler submanifolds, we prove that if M is an umbilical hypersurface of a Minkowski space (V , F ), then either M is a Riemannian space form or a locally Minkowski space. AMS subject classifications: 53C60, 53C40