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Now showing items 1-15 of 15

    • A Wasserstein-like Distance on Vector Fields 

      Sommer, Vincent (2023-10-06)
      We introduce a new distance on the space of vector fields over a Riemannian manifold that is motivated by the construction and properties of the Wasserstein distance. The construction relies on a particular metric on the ...
    • Investigations in Hadamard spaces 

      Bërdëllima, Arian (2021-08-27)
      This thesis investigates the interplay between geometry and convex analysis in Hadamard spaces. Motivated by numerous applications of CAT(0) geometry, our work builds upon the results in convex analysis and Alexandrov ...
    • Bending energy regularization on shape spaces: a class of iterative methods on manifolds and applications to inverse obstacle problems 

      Eckhardt, Julian (2019-12-13)
      In applications such as nondestructive testing, geophysical exploration or medical imaging one often aims to reconstruct the boundary curve of a smooth bounded domain from indirect measurements. As a typical example we ...
    • Generalized Seiberg-Witten and the Nahm Transform 

      Raymond, Robin (2019-01-11)
      Using the viewpoint of principal bundles on hyperk¨ ahler reductions, we recover the results of Gocho and Nakajima [GN92] and give insights into the role that the quater- nions play. We define a framework for dimensional ...
    • New topological and index theoretical methods to study the geometry of manifolds 

      Nitsche, Martin (2018-07-31)
      For a $\mathit{Spin}$ manifold $M$ the Rosenberg index $\alpha([M])$ is an obstruction against positive scalar curvature metrics. When $M$ is non-$\mathit{Spin}$ but $\mathit{Spin}^c$, Bolotov and Dranishnikov suggested ...
    • Origami Cylinders 

      Bös, Friedrich (2018-05-02)
      Origami, the age-old art of folding intricate three-dimensional structures from flat material, has found numerous applications in e.g. the design of deployable structures and mechanical metamaterials.  This thesis ...
    • Variational Estimators in Statistical Multiscale Analysis 

      Li, Housen (2016-05-24)
      In recent years, a novel type of multiscale variational statistical approaches, based on so-called multiscale statistics, have received increasing popularity in various applications, such as signal recovery, imaging and ...
    • Variational Convergence and Discrete Minimal Surfaces 

      Schumacher, Henrik (2015-11-05)
      This work is concerned with the convergence behavior of the solutions to parametric variational problems. An emphasis is put on sequences of variational problems that arise as discretizations of either infinite-dimensional ...
    • Projection Methods in Sparse and Low Rank Feasibility 

      Neumann, Patrick (2015-07-07)
      In this thesis, we give an analysis of fixed point algorithms involving projections onto closed, not necessarily convex, subsets of finite dimensional vector spaces. These methods are used in applications such as imaging ...
    • Analytic singularities near radial points 

      Zheng, Jiguang (2015-03-11)
      In this thesis, we applied tools of algebraic analysis and knowledge of symplectic geometry and contact geometry to give a normal form of certain class of microdifferential operators, and then studied analytic singularities of ...
    • Conformal Properties of Generalized Dirac Operator 

      Thakre, Varun (2013-07-24)
      In this thesis we study the non-linear Dirac operator in dimension four and the associated generalization of the Seiberg-Witten equations in dimension four. The central object of this generalization is a hyperK ahler ...
    • A discrete geometric view on shear-deformable shell models 

      Weischedel, Clarisse (2012-08-15)
      This thesis presents the construction of a geometrically nonlinear shear-deformable (Cosserat type) shell model by methods from discrete differential geometry (DDG). The model aims at applications in real-time simulations ...
    • Membrane locking in discrete shell theories 

      Quaglino, Alessio (2012-05-23)
      This work is concerned with the study of thin structures in Computational Mechanics. This field is particularly interesting, since together with traditional finite elements methods (FEM), the last years have seen the ...
    • Persistence in discrete Morse theory 

      Bauer, Ulrich (2011-07-15)
      The goal of this thesis is to bring together two different theories about critical points of a scalar function and their relation to topology: Discrete Morse theory and Persistent homology. ...
    • Julia Set as a Martin Boundary 

      Islam, Md. Shariful (2010-11-18)
      The Julia set of the class of hyperbolic rational maps having a totally disconnected Julia set is here identified as the Martin boundary of a Markov chain by using symbolic dynamics. When ...