For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis.

Der Praxisleitfaden der Knorpelreparatur richtet sich in erster Linie an operativ tatige Orthopaden, Chirurgen und Unfallchirurgen, die sich speziell uber die modernen Verfahren zur biologischen Gelenkknorpelrekonstruktion informieren mochten. Praktische Hinweise zu den Operationstechniken der Knorpel-Knochen-Transplantation und der Autologen Chondrozytentransplantation werden ebenso vermittelt wie pathophysiologische Grundlagen zur Arthrose. Hinweise zur Diagnostik von Gelenkknorpelschaden mittels MR-Tomographie und praktische Anleitungen zur Begleit- und Nachbehandlung runden dieses Werk ab."

The general approach the author adopted to tackle the whole matter consisted of three broad parts: linear global analysis, non-linear theory and topological classification. For the linear part, the author gathered basic notions from Riemannian geometry, tools from Hilbert space theory, Sobolev spaces and their invariance and finally, uniform pseudo-differential and Fourier integral operators.