-boundedness of oscillating spectral multipliers on Riemannian manifolds
We prove endpoint estimates for operators given by oscillating spectral multipliers on Riemannian manifolds with -bounded geometry and nonnegative Ricci curvature.
Laplace type operators: Dirichlet problem
We investigate Laplace type operators in the Euclidean space. We give a purely algebraic proof of the theorem on existence and uniqueness (in the space of polynomial forms) of the Dirichlet boundary problem for a Laplace type operator and give a method of determining the exact solution to that problem. Moreover, we give a decomposition of the kernel of a Laplace type operator into -irreducible subspaces.
Liouville type theorems for some conformally invariant fully nonlinear equations
This is a report on some joint work with Aobing Li on Liouville type theorems for some conformally invariant fully nonlinear equations.
Local Bounds for Solutions of Higher Order Nonlinear Elliptic Partial Differential Equations.
Lorentz-invariant quantum fields in the space-time tangent bundle.