Elliptic pseudo differential operators degenerate on a symplectic submanifold

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Symplectic geometry and positivity of pseudo-differential operators.

In this paper we establish positivity for pseudo-differential operators under a condition that is essentially also necessary. The proof is based on a microlocalization procedure and a geometric lemma.

Cohomologies and Elliptic Operators on Symplectic Manifolds

In joint work with S.-T. Yau, we construct new cohomologies of differential forms and elliptic operators on symplectic manifolds. Their construction can be described simply following a symplectic decomposition of the exterior derivative operator into two first-order differential operators, which are analogous to the Dolbeault operators in complex geometry. These first-order operators lead to ne...

on the spectral properties of degenerate non-selfadjoint elliptic systems of differential operators

Hardy Type Inequalities Related to Degenerate Elliptic Differential Operators

We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators Lpu := −∇ ∗ L(|∇Lu| ∇Lu). If φ is a positive weight such that −Lpφ ≥ 0, then the Hardy type inequality c ∫ Ω |u| φp |∇Lφ| p dξ ≤ ∫