CR-invariants and the scattering operator for complex manifolds with boundary

Cr-invariants and the Scattering Operator for Complex Manifolds with Boundary

Minimality in CR geometry and the CR Yamabe problem on CR manifolds with boundary

We study the minimality of an isometric immersion of a Riemannian manifold into a strictly pseudoconvex CR manifold M endowed with the Webster metric (associated to a fixed contact form on M), hence formulate a version of the CR Yamabe problem for CR manifolds-with-boundary. This is shown to be a nonlinear subelliptic problem of variational origin.

Complex cobordism and embeddability of CR-manifolds

This paper studies complex cobordisms between compact, three dimensional, strictly pseudoconvex Cauchy-Riemann manifolds. Suppose the complex cobordism is given by a complex 2-manifold X with one pseudoconvex and one pseudoconcave end. We answer the following questions. To what extent is X determined by the pseudoconvex end? What is the relation between the embeddability of the pseudoconvex end...

Eigenvalues of the Dirac Operator on Manifolds with Boundary

Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. For the local boundary conditions, limiting cases are characterized by the existence of real Killing spinors and the minimality of the boundary.

The Complex Gradient Operator and the CR-Calculus

Often signals and system parameters are most conveniently represented as complex-valued vectors. This occurs, for example, in array processing [1], as well as in communication systems [7] when processing narrowband signals using the equivalent complex baseband representation [2]. Furthermore, in many important applications one attempts to optimize a scalar real-valued measure of performance ove...