Spectral minimal partitions on metric graphs
A talk in the Oberseminar Analysis series by
Delio Mugnolo from Hagen
| Abstract: | We introduce a new partitioning approach focusing on metric graphs, building upon the theory of spectral minimal partitions developed over the past 20 years. While previous work has primarily examined domains, our focus is on the partitioning of metric graphs. We establish the existence of spectral minimal partitions by demonstrating that a suitable (non-convex) lower semicontinuous functional, supported on a metric space of metric graph partitions, attains a minimum. Although the topology of metric graphs poses challenges compared to domains, it also reveals intriguing new features of these structures. Additionally, time permitting, we will explore partitioning approaches based on thermal insulation and heat content. This research is a collaborative effort involving Patrizio Bifulco, Matthias Hofmann, James Kennedy, Pavel Kurasov, Corentin Léna, and Marvin Plümer. Zoom Meeting ID: 622 2841 8411 Passcode: 058508 $\href{https://uni-bielefeld.zoom.us/j/62228418411?pwd=bkNteGxqMGFRemZhOWRwek1tNGtkUT09}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): A8 |