In this thesis, a novel discrete approximation of the curvature tensor on Riemannian manifolds is derived, efficient methods to interpolate and extrapolate images in the context of the time discrete metamorphosis model are ...

Based on the theoretical framework recently proposed by Bonifacius and Neitzel (2018) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a ......

In this thesis, we study the moduli spaces M_(g,q)^m (G)of flat pointed principal G-bundles over Riemann surfaces X. The genus of X is g 0 and G is a fixed Lie group. Further, we are given m 0 permutable marked points in ...

This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution-free ......

In this thesis we are concerned with developing a systematic framework for dealing with the Carleson and the Variational Carleson Operators. We extend the framework of outer measure Lp spaces of Do and Thiele to an iterated ...

This thesis is concerned with questions arising in the realm of mirror symmetry for K3 surfaces. It is divided into two parts.
In the first part, we study the bijection between Fourier–Mukai partners of a K3 surface ...

We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number κ in bounded domains in ℝ^d. The discrete trial and test spaces are ......

In this thesis we prove generalized lower Ricci curvature bounds in the sense of optimal transport for warped products and cones over metric measure spaces, and we prove a maximal diameter theorem in this context.
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We study cohomology Bott manifolds by means of modified surgery theory. Cohomology Bott manifolds admit a ring isomorphism to the cohomology ring of a Bott manifold which preserves the Pontrjagin and Stiefel-Whitney classes. ...

This thesis is concerned with two special cases of the singular Brascamp-Lieb inequality, namely, the trilinear forms corresponding to the one- and two-dimensional bilinear Hilbert transform. In this work we study the ...