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  Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity

Jasiulek, M., & Korzynski, M. (2012). Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity. Classical and quantum gravity, 29(15): 155010. doi:10.1088/0264-9381/29/15/155010.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0012-5E29-2 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0015-7BD9-4
Genre: Journal Article

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1111.6523 (Preprint), 772KB
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 Creators:
Jasiulek, Michael1, Author           
Korzynski, Mikolaj2, Author           
Affiliations:
1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24013              
2Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: We present a numerical method for solving Weyl's embedding problem which consists of finding a global isometric embedding of a positively curved and positive-definite spherical 2-metric into the Euclidean three space. The method is based on a construction introduced by Weingarten and was used in Nirenberg's proof of Weyl's conjecture. The target embedding results as the endpoint of an embedding flow in R^3 beginning at the unit sphere's embedding. We employ spectral methods to handle functions on the surface and to solve various (non)-linear elliptic PDEs. Possible applications in 3+1 numerical relativity range from quasi-local mass and momentum measures to coarse-graining in inhomogeneous cosmological models.

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 Dates: 2011-11-282012
 Publication Status: Issued
 Pages: 18 pages, 14 figures
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 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1111.6523
URI: http://arxiv.org/abs/1111.6523
DOI: 10.1088/0264-9381/29/15/155010
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Title: Classical and quantum gravity
Source Genre: Journal
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Publ. Info: Bristol, U.K. : Institute of Physics
Pages: - Volume / Issue: 29 (15) Sequence Number: 155010 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: https://pure.mpg.de/cone/journals/resource/954925513480_1