A conformally invariant sphere theorem in four dimensions
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
A fully nonlinear version of the Yamabe problem on manifolds with boundary
We propose to study a fully nonlinear version of the Yamabe problem on manifolds with boundary. The boundary condition for the conformal metric is the mean curvature. We establish some Liouville type theorems and Harnack type inequalities.
A minimization problem arising from prescribing scalar curvature functions.
Algebraically independent generators of invariant differential operators on a symmetric cone.
An expression of classical dynamics
An -isolation theorem for Yang-Mills fields