dc.contributor.advisor Bartsch, Thomas dc.contributor.advisor Ahmedou, Mohameden dc.contributor.author Fiernkranz, Tim dc.date.accessioned 2021-12-08T14:31:17Z dc.date.available 2021-12-08T14:31:17Z dc.date.issued 2021 dc.identifier.uri https://jlupub.ub.uni-giessen.de//handle/jlupub/371 dc.identifier.uri http://dx.doi.org/10.22029/jlupub-307 dc.description.abstract For $2\le N\in \N$ and $\G_i\in \R\setminus\{0\}$ we proof that functions of the form de_DE $$H_\G (p_1,\dots, p_N) = \sum_{i\ne j} \G_i\G_j G(p_i,p_j) + \sum_{i=1}^N \G_i^2 R(p_i) ,$$ admit critical points under various circumstances. The $p_i$ will either belong to an open, bounded subset $\gO\subset \R^d$ with smooth boundary for $d \ge 3$ or to a compact, two dimensional, riemanian manifold $(\gS ,g )$. Furthermore, $G$ is a (Dirichlet) Green's function of the negative Laplacian $-\gD$ associated to $\gO$ or $(\gS, g)$ and $R$ is its Robin's function.\\ For the case of an open set, we also consider the function $\gr$ that is the least eigenvalue of the matrix $$(M(x_1,\dots,x_N))_{i,j=1}^N := \begin{cases} -G(x_i , x_j),& i\ne j\\ R(x_i),& i=j . \end{cases}$$ To achieve the critical points, we also calculate appropriate approximations of the Green's function and Robin's function when close to their singularities. dc.language.iso en de_DE dc.subject Critical Points de_DE dc.subject Vortex Dynamics de_DE dc.subject Greens Function de_DE dc.subject.ddc ddc:510 de_DE dc.title Critical Points of Kirchhoff-Routh-Type Functions de_DE dc.type doctoralThesis de_DE dcterms.dateAccepted 2021-11-02 local.affiliation FB 07 - Mathematik und Informatik, Physik, Geographie de_DE thesis.level thesis.doctoral de_DE
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