Boundary value problems and index theory on Riemannian and Lorentzian manifolds

点击翻译按钮获取中文摘要

Building on the results of the previous project “Index theory on Lorentzian manifolds” it is planned to investigate boundary value problems and index theory for first order operators in both the Riemannian and the Lorentzian setting. This emcompasses the derivation of geometric index formulas for general first-order elliptic operators on manifolds with boundary, relative index theory à la Gromov and Lawson, boundary value problems for non-compact and non-smooth boundary, higher index theory and Callias-type operators on the Riemannian side. On Lorentzian manifolds we investigate local index theory for Dirac-type and more general operators, initial-boundary value problems and the characteristic initial value problem for Dirac operators.