de.mpg.escidoc.pubman.appbase.FacesBean
English
 
Help Guide Disclaimer Contact us Login
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Flowing maps to minimal surfaces: Existence and uniqueness of solutions

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons61163

Rupflin,  M.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)

1205.6982
(Preprint), 315KB

AIHP31_349.pdf
(Any fulltext), 390KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Rupflin, M., & Topping, P. (2014). Flowing maps to minimal surfaces: Existence and uniqueness of solutions. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 31, 349-368. doi:10.1016/j.anihpc.2013.03.008.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-D24E-D
Abstract
We study the new geometric flow that was introduced in [11] that evolves a pair of map and (domain) metric in such a way that it changes appropriate initial data into branched minimal immersions. In the present paper we focus on the existence theory as well as the issue of uniqueness of solutions. We establish that a (weak) solution exists for as long as the metrics remain in a bounded region of moduli space, i.e. as long as the flow does not collapse a closed geodesic in the domain manifold to a point. Furthermore, we prove that this solution is unique in the class of all weak solutions with non-increasing energy. This work complements the paper [11] of Topping and the author where the flow was introduced and its asymptotic convergence to branched minimal immersions is discussed.