On the Gauss equation of a minimal immersion in 3-dimensional hyperbolic manifold
Marcello Lucia (CUNY, New York)
- https://www.uni-giessen.de/de/fbz/fb07/fachgebiete/mathematik/mathematik/kalender/2022/2022-06-13
- On the Gauss equation of a minimal immersion in 3-dimensional hyperbolic manifold
- 2022-06-13T16:15:00+02:00
- 2022-06-13T17:15:00+02:00
- Marcello Lucia (CUNY, New York)
13.06.2022 von 16:15 bis 17:15 (Europe/Berlin / UTC200)
Hörsaal (1. Stock, Raum 111) im Mathematischen Institut, Arndtstraße 2
Abstract:
We consider the Gauss equation that governs the minimal immersion of a closed surface of genus greater than two in a three dimensional hyperbolic manifold for which the second fundamental form is prescribed.
The PDE admits two solutions and we will analyze the behavior of such solutions when the norm of the second fundamental form is small. In the genus two case, we will see that only one solution arises from a minimal immersion if the three dimensional manifold is complete.