We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth as long as the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists for all times and the network converges to the Steiner minimal connection between the three endpoints.
Motion by curvature of planar networks, II
NOVAGA, MATTEO
2016-01-01
Abstract
We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth as long as the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists for all times and the network converges to the Steiner minimal connection between the three endpoints.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
Arpi 817343.pdf
accesso aperto
Tipologia:
Documento in Post-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
407.29 kB
Formato
Adobe PDF
|
407.29 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.