Hearing pseudoconvexity with the Kohn Laplacian

Hearing Pseudoconvexity with the Kohn Laplacian

A bounded domain in C with connected Lipschitz boundary is pseudoconvex if the bottom of the essential spectrum of the Kohn Laplacian on the space of (0, q)-forms, 1 ≤ q ≤ n− 1, with L-coefficients is positive.

A New Characterization of the Cr Sphere and the Sharp Eigenvalue Estimate for the Kohn Laplacian

On Strict Pseudoconvexity

The present paper provides first and second-order characterizations of a radially lower semicontinuous strictly pseudoconvex function f : X → R defined on a convex setX in the real Euclidean space Rn in terms of the lower Dini-directional derivative. In particular we obtain connections between the strictly pseudoconvex functions, nonlinear programming problem, Stampacchia variational inequality...

Propagation of Regularity for Solutions of the Kohn Laplacian in a Flat Boundary

We prove that CR lines in an exponentially degenerate boundary are propagators of holomorphic extension. This explains, in the context of the CR geometry, why in this situation the induced Kohn-Laplacian b is not hypoelliptic (Christ [3]). MSC: 32F10, 32F20, 32N15, 32T25

Hypoellipticity of the Kohn Laplacian for Three-dimensional Tubular Cr Structures

(1) ∂̄b = ∂x + i(∂y − φ(x)∂t) where φ ∈ C∞(R) is real-valued. Such CR structures may be realized as the boundaries of tube domains {z : Im z2 > φ(Re z1)} in C. The Levi form may be identified with the function φ′′(x). We always assume that φ is convex, so that the structure is pseudoconvex. By ∂̄∗ b we mean the adjoint of ∂̄b with respect to L (R, dx dy dt); thus ∂̄∗ b = −∂x + i(∂y − φ(x)∂t). The p...