The analytic dilation method was originally used in the context of many body Schrödinger operators. In this thesis we adapt it to the context of compatible Laplacians on complete manifolds with corners of codimension two. ...

Suppose S is an oriented, compact surface with genus at least two. This thesis investigates the \homology curve complex" of S; a modification of the curve complex first studied by Harvey in which the verticies are required to be homologous multicurves. The relationship between arcs in the homology curve graph and surfaces with boundary in S x R is used to devise an algorithm for constructing efficient arcs in the homology multicurve graph. Alternatively, these arcs can be used to study oriented surfaces with boundary in S x R. The intersection number of curves in S x R is defined by projecting curves into S. It is proven that the best possible bound on the distance between two curves c₀ and c₁ in the homology curve complex depends linearly on their intersection number, in contrast to the logarithmic bound obtained in the curve complex. The difference in these two results is shown to be partly due to the existence of what Masur and Minsky refer to as large subsurface projections of c₀ and c₁ to annuli, and partly due to the small amount of ambiguity in defining this concept. A bound proportional to the square root of the intersection number is proven in the absence of a certain type of large subsurface projection of c₀ and c₁ to annuli....

(co)homology is an important tool for studying spaces with a group action. These (co)homology groups are defined via the Borel construction. For discrete group they can also be defined in terms of homological algebra. One ...

Diese Arbeit befasst sich mit Dünngitterverfahren zur Lösung von höherdimensionalen Problemen. Sie zeigt drei neue Aspekte von Dünnen Gittern auf: Erweiterungen der elementaren Werkzeuge zur Arbeit mit Dünnen Gittern, eine ...

This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or ...

In many medical and technical applications, numerical simulations need to be performed for objects with interfaces of geometrically complex shape. We focus on the biomechanical problem of elasticity simulations for trabecular ...

VLSI placement is one of the major steps in the chip design process and an interesting subject of research in industry and academia. Recent chips consist of several millions of circuits connected by millions of nets. The ...

In dieser Arbeit stellen wir erstmalig einen parallelen Löser für inkompressible Zweiphasenströmungen mit Oberflächenspannung in drei Raumdimensionen vor, der Masseerhaltung und hohe Konvergenzordnung vereint. Als zweite ...

In this thesis we study Fourier-Mukai transforms between derived categories of twisted sheaves. We show that some well known results about the classification of surfaces under derived categories extend to the derived ...

In dieser Arbeit beschäftigen wir uns mit der Modellierung und Existenztheorie von dünnen Filmen inkompressibler, viskoser Flüssigkeiten auf evolvierenden, d.h. sich bewegenden, gekrümmten Flächen. Dünne Filme treten in ...