Elliptic-hyperbolic systems and the Einstein equations
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There exists a harmonic map homotopic to the identity, and such a map is an orientation-preserving diffeomorphism.
“From [34, 35], we know that there is a harmonic map homotopic to the identity i.e., E ∈ D 0 and in fact such a map is an orientation preserving diffeomorphism.”
From Big-bang limit of 2 + 1 gravity and Thurston boundary of Teichmüller space (2023) · cites this paper as [34]
Section 1.1 states that the identity map is harmonic when the spatial-harmonic gauge condition V = 0 holds. The identity is an orientation-preserving diffeomorphism, but the paper does not establish the claimed general existence of a harmonic map homotopic to the identity. (LLM, conf=0.78)
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Research works printed but not linked: 6
- Helmut Friedrich and Alan Rendall, The Cauchy problem for the Einstein equations, Einstein's field equations and their physical implications, Springer, Berlin, 2000, pp. 127-223.
- Tosio Kato, Abstract evolution equations, linear and quasi-linear, revisited, Functional analysis and related topics, 1991 (Kyoto), Springer, Berlin, 1993, pp. 103-125.
- A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences, vol. 53, Springer-Verlag, New York, 1984.
- Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York, 1973, McGraw-Hill Series in Higher Mathematics.
- Winfried Sickel, Composition operators acting on Sobolev spaces of fractional order -a survey on sufficient and necessary conditions, Function spaces, differential operators and nonlinear analysis (Paseky nad Jizerou, 1995), Prometheus, Prague, 1996, pp. 159-182.
- Christopher D. Sogge, Lectures on nonlinear wave equations, International Press, Boston, MA, 1995.
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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
- Andersson, L., & Moncrief, V.
- Affiliations
- University of Miami (US)
- Yale University (US)
- ORCID
- Andersson, L.
- Venue
- Annales Henri Poincaré
- Published
- 2003-03
- Volume
- 4
- Issue
- 1
- Pages
- 1-34
- ISSN
- 1424-0637 (ISSN-L)
- 1424-0661
- OpenAlex
- W2073243744
- Cited by
- 168
- References
- 0
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 6 · 2023: 7 · 2022: 3 · 2021: 7 · 2020: 10 · 2019: 6 · 2018: 5 · 2017: 4 · 2016: 4 · 2015: 6 · 2014: 4 · 2013: 2 · 2012: 8
- FWCI
- 3.77
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Annales Henri Poincaré (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0098084, 0104402, 9732629)
- Institut des Hautes Études Scientifiques, Université Paris-Saclay
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Mathematical Physics Problems
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- elliptic-hyperbolic systems, Cauchy problem, local well-posedness, continuation principle, vacuum spacetimes, gauge fixing
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