E-Dissertationen: Suche
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Linear Inviscid Damping for Monotone Shear Flows, Boundary Effects and Sharp Sobolev Regularity
(2015-07-23)
In this thesis, we study the linear stability and long-time asymptotic behavior of solutions to the 2D incompressible Euler equations, which model the evolution of an inviscid, incompressible fluid.
The Euler equations ...
The Euler equations ...
Stable maps and singular curves on K3 surfaces
(2015-08-05)
This thesis develops and applies the theory of arbitrary genus stable maps to K3 surfaces. In the first application of the theory, we study the loci of smooth curves of genus p-n admitting n-nodal models on K3 surfaces. ...
Parallel RBF Kernel-Based Stochastic Collocation for Large-Scale Random PDEs
(2015-07-03)
In this thesis, the solution of large-scale uncertainty quantification problems is considered. Uncertainty quantification aims to extract stochastic (moment) information from processes with uncertain input data. These ...
Hilbert transforms and maximal operators along planar vector fields
(2015-07-16)
In harmonic analysis, there is a conjecture (attributed to Zygmund) stating that the directional maximal operator along a Lipschitz planar vector field is weakly bounded on L^2. In this thesis, we present some recent ...
Singular propagators in deformation quantization and Shoikhet-Tsygan formality
(2015-06-03)
This thesis adds some details to the seminal approach to logarithmic formality and interpolation formality by Alekseev, Rossi, Torossian and Willwacher: We prove that the interpolation family of Kontsevich formality maps ......
Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds
(2015-11-12)
In this thesis we study the Selberg and Ruelle zeta functions on compact oriented hyperbolic manifolds
X of odd dimension d. We prove that they converge in some half-plane Re(s)>c and that they admit a meromorphic ...
X of odd dimension d. We prove that they converge in some half-plane Re(s)>c and that they admit a meromorphic ...
Thin Viscous Films on Curved Geometries
(2014-08-29)
The topic of this thesis is the evolution of thin viscous films on curved substrates. Using techniques from differential geometry, namely the exterior calculus of differential forms, and from optimization theory, in ...
Factorization of holomorphic eta quotients
(2014-12-12)
We conjecture the occurrence of a certain type of factor of a holomorphic eta quotient whenever it is reducible and we prove this conjecture for all prime power levels. In particular, this also implies that rescaling and ...
L2-index theory, the Chern conjecture, and manifolds of special holonomy
(2014-12-12)
In this dissertation we study a conjecture attributed to Chern and Hopf, a generalization of Atiyah's L2-index theorem used by Gromov to prove said conjecture for Kähler manifolds, and an extension to Kähler ......
Flat Fronts and Stability for the Porous Medium Equation
(2014-08-26)
This work shows stability of general solutions of the porous medium equation close to flat travelling wave fronts in the sense of homogeneous Lipschitz spaces under rather weak conditions on the initial data that are optimal ...