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  Flowing maps to minimal surfaces: Existence and uniqueness of solutions

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-D24E-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-36C7-9
Genre: Journal Article

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1205.6982 (Preprint), 315KB
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 Creators:
Rupflin, M.1, Author              
Topping, P., Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24012              

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Free keywords: Mathematics, Differential Geometry, math.DG,Mathematics, Analysis of PDEs, math.AP,
 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.

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 Dates: 2012-05-3120122014
 Publication Status: Published in print
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 Identifiers: arXiv: 1205.6982
DOI: 10.1016/j.anihpc.2013.03.008
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Title: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Source Genre: Journal
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Pages: - Volume / Issue: 31 Sequence Number: - Start / End Page: 349 - 368 Identifier: -