dc.rights.license | CC-BY-NC-ND | |
dc.contributor | A. del Pino | |
dc.contributor.advisor | Pino Gomez, A. del | |
dc.contributor.author | Cristinelli, Giacomo Cristinelli | |
dc.date.accessioned | 2022-04-13T00:00:56Z | |
dc.date.available | 2022-04-13T00:00:56Z | |
dc.date.issued | 2022 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/41490 | |
dc.description.abstract | Anisotropic deformation, sometimes generically called adiabatic deformation, is a metric blow-up that is natural to construct on contact manifolds. Such manifolds admit a Riemannian metric which is adapted to the contact distribution in the following sense: the metric $g$ consists of a horizontal part $g_h$, that comes from a subRiemannian structure on the tangent distribution, and another one $g_v$ on the vertical direction. The deformation then rescales the metric by a factor of $1/\epsilon^2$ on the vertical component. Every variation of the value of $\epsilon$, especially in the limit $\epsilon\to 0$, massively affects almost every metric-dependent attribute of the manifold. Gromov proved that the induced metric space converges in the Gromov-Hausdorff sense to the subRiemannian one.
This thesis is a collection of recent results and possible future developments in the study of anisotropic limits. It starts with a description of some geometrical features of the anisotropic limit, namely the convergence of some Riemannian geodesics to Reeb orbits through \textit{spiraling} subRiemannian geodesics. Then the discussion continues with the study of the perturbation of some Laplace and Dirac-type operators. The purpose is to analyze the convergence of such operators in the resolvent sense. | |
dc.description.sponsorship | Utrecht University | |
dc.language.iso | EN | |
dc.subject | We studied the convergence of geodesics to Reeb orbits under anisotropic deformation on closed contact three-dimensional manifolds and its relation with the spectral properties of the Hodge-Laplacian. | |
dc.title | Anisotropic deformation on contact three-manifolds | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | Contact geometry; subRiemannian geometry; Reeb dynamics; | |
dc.subject.courseuu | Mathematical Sciences | |
dc.thesis.id | 3326 | |