Boris Yu. Sternin

Differential equations on complex manifolds

We discuss linear partial differential equations with constant coefficients on complex manifold \( \mathbb{C}^n \). Using the Sternin–Shatalov integral transform we solve complex Cauchy problem and consider two applications: describe the singularities of the solution of the Cauchy problem and solve a physical problem of sweeping the charge inside the domain (balayage inwards problem).

On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem

We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.