At the beginning of this work the interest in the community has focussed on the pancake picture proposed by Zel'dovich and the Russian school. At that time, Sergei Shandarin has produced some numerical simulations in two spatial dimensions and applied together with Arnol'd and Zel'dovich the Lagrange-singularity theory to identify the building blocks of large-scale structure in these simulations. The first high-resolution plots of pancakes in 2D (Refs. P2,C1,C2,C7) and discussions with Sergei at the MPA were the motivation to start this thesis on the three-dimensional implementation of high-resolution methods. Some results of this thesis have been presented on workshops (e.g., Refs. C6,C9) and were joined together with subsequent work in a larger paper (Ref. P20). (See also Refs. P5,C12,C15.)

(D2) Arno Weiss: Simulation und statistische Analyse strahlenförmiger Galaxienkataloge im dreidimensionalen Pancake-Modell (LMU Munich, May 1992)

Based on the ideas of the previous thesis, Arno Weiss probed pencil beam model observations through three-dimensional high-resolution pancake simulations. This work was prepared by a two-dimensional study (Ref. P4). The goal was to explain on a statistical basis the `periodicity-scale' identified by Broadhurst and Szalay in a deep pencilbeam survey. He succeeded to find enough beams that show a typical scale of 60 Mpc/h, but also some with the periodicity-scale reported by the observational group. On the basis of this work we designed an observational proposal (proposed to the ESO observatory) suggesting an optimal choice of a two-beam survey. The article (Ref. P12; see also C17) summarizes the results of this thesis which were among the first to explain naturally (i.e. without invoking artificial periodicity input) the observed pencilbeam features.

(D3) Udo Weigelt: ... (LMU Munich, ...)

(D4) Matthias Vanselow: Verallgemeinerung von kosmologischen Lösungen im Rahmen der Lagrangeschen Störungstheorie (LMU Munich, May 1995)

Thus far, the Lagrangian perturbation theory has been developed up the the third order (Ref. P14). We were interested to eventually find a closed formula for the n-th order perturbation solutions. Also, from a phenomenological perspective, we knew that the second-order solutions display a second `shell-crossing' singularity (in N-body simulations a whole hierarchy of such shell-crossings has been observed), while the third-order solutions only redistribute the mass inside the second shell. To go beyond third-order could reveal the missing systematics in the perturbation series and eventually answer the question of its convergence. The work by Matthias was focussed on explicit solutions also for other background cosmologies at higher-order. He formulated explicit general solutions for third-order perturbations on curved backgrounds as well as the fourth-order solution on an Einstein-de Sitter background. This work is unpublished. Systematizing the n-th order scheme was put forward in a review with Jürgen Ehlers (Ref. P24).

(D5) Michael Platzöder: Statistische Analyse der Galaxienverteilung mit Hilfe von Minkowski-Funktionalen (LMU Munich, June 1995)

The suggestion of employing Minkowski-functionals for the morphometry of cosmic structure (Ref. ...) was the motivation to analyze some N-body simulations and to develop detailed tools of pattern recognition (to identify sheets, filaments and clusters) that are based on the Minkowski-functionals. Michael's work contributed to a clarification of the range of applicability of the new tools. Some material was published in (Ref. C19).

(D6) Jens Schmalzing: Robuste morphologische Masse für grossräumige Strukturen im Universum (LMU Munich, September 1996)

As a member of the newly founded group at the LMU within a SFB project of the DfG (German Science Foundation), Jens established rigorously the use of Minkowski-functionals for the analysis of data sets in cosmology. He developed new software and extended the scope of applications substantially. A generalization and unification of a topological statistics known as `genus statistics' applied to isodensity contours of cosmic density fields was one of the highlights of his thesis. (Refs. P25, C24,C26).

(D7) Claus Beisbart: Morphologie und Dynamik kosmischer Materieaggregationen (LMU Munich, July 1997)

Working in the same group as Jens, Claus established further generalizations such as vector-valued Minkowski-functionals and applied them to galaxy cluster data (C31). Besides contributing many further insights into the Minkowski framework, a second focus of his thesis was the dynamical understanding of galaxy clusters. Within the framework of the velocity moment hierarchy of a kinetic description of self-gravitating systems, he studied adhesion-type structure formation models, and he especially concentrated on generalizations of the virial theorem for non-isolated bodies.

(D8) Andreas Rabus: Anwendung morphologischer Masse auf Simulationen dunkler Materie und auf Galaxienkataloge (LMU Munich, August 1998)

Andreas' work was mainly concerned with numerical implementations of Minkowski-functionals for the purpose of applying them to large data sets that are, e.g., provided by large N-body simulations. In particular, he used the concept of Partial Minkowski-functionals.

(D9) Christian Sicka: Hierarchische Kosmologien, Mittelungsproblem und Skalierungseigenschaften (LMU Munich, November 1998)

Hierarchical cosmologies held a conceptually important status before the homogeneous-isotropic standard model succeeded better in explaining observational data. Using modern language, Christian reviewed the history of Charlier-type models and studied a more general framework for averaged inhomogeneous cosmologies within which, in principle, one could study hierarchical as well as homogeneous world models. Besides this, however, the thesis was in a large part concerned with explicit calculations of the so-called `backreaction' source for the effective evolution of world models. These models were constructed with the help of analytical approximations for the evolution of inhomogeneities, and boundary conditions were employed such that the effective model obeys the standard Friedmann equation on the largest scale (see Refs. P34,C33).

(D10) Stephan Lante: Zur relativistischen Erweiterung kosmologischer Modelle der Strukturbildung (LMU Munich, March 2000)

The success of a Lagrangian description of fluid motion in Newtonian cosmology was the motivation to study Einstein's equations along the same lines. Within the ADM formulation of general relativity, and using Cartan's method, the analogy of a Lagrangian description was established in this thesis. Reformulating the ADM equations in terms of deformation one-forms, it was shown that the Lagrangian evolution equations in the Newtonian framework correspond to a formally similar subset of evolution equations for the deformation one-forms. A deeper understanding of this subset of the ADM equations (that reduces to the Newtonian equations in the case of exact one-forms) could be obtained in terms of the electric part of the Weyl tensor. Relativistic generalizations of Zel'dovich's approximation have been put into perspective (see Ref. P44).

(D11) Matthias Ostermann: Grundlagen der Formulierung einer Lagrangeschen Störungstheorie in der relativistischen Kosmologie (LMU Munich, May 2003)

...

(D12) Alexander Wiegand: Ein skalendifferenziertes Entwicklungsmodell des inhomogenen Universums (Universität Karlsruhe, October 2009)

....

The Lagrangian perturbation approach, originally formulated for the dust matter model, has been generalized to perfect fluids. The Lagrangian evolution equations for this class of matter models was investigated and solved to first order. The relation of this solution to the `adhesion model' and other consequences for the description of structure formation have been discussed (Ref. P31).

(P2) Arno Weiss: Numerische und statistische Verfahren zur kosmologischen Simulation der grossräumigen Galaxienverteilung unter Verwendung der Lagrangeschen Störungsrechnung (LMU Munich, August 1995)

(P3) Georgios Karakatsanis: Optimierung der Lagrangeschen Störungstheorie für die analytische Simulation kosmologischer Strukturen (LMU Munich, August 1995)

(P4) Robert Klaffl: Numerical simulations of large-scale structure (student left for a job before finalizing the thesis)

(P5) Udo Weigelt: Robuste statistische Analyse stark fehlerbehafteter Datensätze und Anwendungen auf Pekulargeschwindigkeitskataloge (LMU Munich, ... 1996)

(P6) Martin Kerscher: Morphologie grossräumiger Strukturen im Universum (LMU Munich, January 1998)

(P7) Jens Schmalzing: On statistics and dynamics of cosmic structure (LMU Munich, September 1999)

(P8) Claus Beisbart: Measuring cosmic structure. Minkowski valuations and mark correlations for cosmological morphometry (LMU Munich, November 2000)

(P9) Christian Sicka: Effektive Dynamik inhomogener Kosmologien (LMU Munich, May 2003)

...

(P10) Matthias Ostermann: Minkowski valuations of the Sloan Digital Sky Survey and Lagrangian theory of structure formation in relativistic cosmology (LMU Munich, expected end: 2011)