Asymptotics of the Teichmüller harmonic map flow
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[37] proved a local well-posedness theorem for the Cauchy problem for a family of elliptic-hyperbolic systems that included the n+1 dimensional vacuum Einstein equations in CMCSH gauge, n >= 2.
“[37] proved a local well-posedness theorem for the Cauchy problem for a family of elliptichyperbolic systems that included the ' n + 1 ' dimensional vacuum Einstein equations in CMCSH gauge, n ≥ 2 .”
From Big-bang limit of 2 + 1 gravity and Thurston boundary of Teichmüller space (2023) · cites this paper as [37]
The Introduction (page unavailable) describes the Teichmüller harmonic map flow, and Section 3 studies its asymptotic convergence. Searches for CMCSH gauge, the vacuum Einstein equations, and local well-posedness found no passage addressing the claimed theorem in our copy. (LLM, conf=0.78)
Experimental — accuracy not yet measured[37] also proved conservation of gauges and constraints.
“They also proved the conservation of gauges and constraints.”
From Big-bang limit of 2 + 1 gravity and Thurston boundary of Teichmüller space (2023) · cites this paper as [37]
Section 3 discusses energy decay and asymptotic convergence of the Teichmüller harmonic map flow; Remark 2.3 discusses preservation of norms of quadratic differentials. Neither addresses conservation of gauges or constraints. Searches for those terms and their preservation found no supporting passage in our copy. (LLM, conf=0.72)
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Cites
The irreducibility of the space of curves of given genus
Deligne, P., & Mumford, D. (1969) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684599 · Cited by 1,763 · see citing works
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Research works printed but not linked: 4
- F. P. Gardiner: Teichmüller theory and quadratic differentials. Pure and Applied Mathematics (New York). A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1987. xviii+236 pp.
- D. Mumford, A Remark on Mahler's Compactness Theorem. Proc. Amer. Math. Soc. 28 (1971) 289-294.
- M. Rupflin and P.M. Topping, Flowing maps to minimal surfaces, preprint (2012), http://arxiv.org/abs/1205.6298 · arXiv
- M. Rupflin, Flowing maps to minimal surfaces: Existence and uniqueness of solu- tions, preprint (2012) http://arxiv.org/abs/1205.6982 · arXiv
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Big-bang limit of 2 + 1 gravity and Thurston boundary of Teichmüller space
Mondal, P. (2023) · Journal of Mathematical Physics · doi:10.1063/5.0136631 · Cited by 1 · see citing works
- Authors
- Rupflin, M., Topping, P. M., & Zhu, M.
- Affiliations
- Max Planck Institute for Gravitational Physics (DE)
- University of Warwick (GB)
- Max Planck Institute for Mathematics in the Sciences (DE)
- Corresponding author
- Rupflin, Melanie
- Venue
- Advances in Mathematics
- Publisher
- Elsevier BV
- Published
- 2013-09
- Volume
- 244
- Pages
- 874-893
- ISSN
- 0001-8708 (ISSN-L)
- OpenAlex
- W1838552752
- Cited by
- 20
- References
- 1
- Citations by year
- 2023: 3 · 2022: 1 · 2020: 3 · 2018: 4 · 2017: 2 · 2016: 3 · 2014: 2 · 2013: 1 · 2012: 1
- FWCI
- 3.36
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Advances in Mathematics (publishedVersion)
- Oxford University Research Archive (ORA) (University of Oxford) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- arXiv (Cornell University)
- Funders
- The Leverhulme Trust
- EPSRC (EP/K00865X/1)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- harmonic maps, holomorphic quadratic differentials, degenerate metrics, Riemann surfaces, constant curvature metrics, asymptotic behavior, geometric analysis
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