Thomas Schick: Bounded Geometry and L2-index theorem

• The analysis of manifolds with boundary and of bounded geometry, and the development of an L2-index theorem for manifolds with boundary (as generalization of Atiyah's L2-index theorem) are the two main subjects of my dissertation Analysis on boundary manifolds of bounded geometry, Hodge-de Rham isomorphism and L2-index theorem (abstract).
• Part of this work was later updated. The result are three newer papers:
• Geometry and Analysis of Boundary-Manifolds of Bounded Geometry (abstract), which describes the geometry of manifolds of bounded geometry and contains e.g. a strong Bochner type vanishing theorem
• Boundary manifolds of bounded geometry (abstract), where some technical properties of these manifolds are established
• L2-index theorem for Boundary-Manifolds (abstract)