Hearing Pseudoconvexity with the Kohn Laplacian

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

Local Solvability in Top Degree of the Semilinear Kohn Equation

We study the local solvability problem for a class of semilinear equations whose linear part is the Kohn Laplacian, acting on top degree forms. We also study the validity of the Poincaré lemma, in top degree, for semilinear perturbations of the tangential Cauchy-Riemann complex.

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

The 1-Laplacian, the ∞-Laplacian and Differential Games

This paper considers the p-Laplacian PDE for p = 1,∞ and some interesting new game theoretic interpretations, due to Kohn–Serfaty [K-S] and to Peres–Schramm–Sheffield–Wilson [P-S-S-W].

Sharp L-bounds for the Wave Equation on Groups of Heisenberg Type

Consider the wave equation associated with the Kohn Laplacian on groups of Heisenberg type. We construct parametrices using oscillatory integral representations and use them to prove sharp L and Hardy space regularity results.