Results 41 to 50 of about 4,657,305 (302)
Ancient solutions to the Ricci flow in dimension $3$ [PDF]
Acta Mathematica, 2018 It is known from work of Perelman that any finite-time singularity of the Ricci flow on a compact three-manifold is modeled on an ancient $\kappa$-solution.
S. Brendle
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PMC Physics A, 2007 15 pages. V2: improved presentation, in particular Jordan vs. Brans-Dicke and on viability. Added section on physical interpretation. V3: more references.
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A Derivation of the Ricci Flow
Journal of Applied Mathematics and Physics, 2021 In this work, we show that by restricting to the subgroup of time-independent coordinate transformations, then it is possible to derive the Ricci flow from the Bianchi identities. To achieve this, we first show that the field equations of the gravitational field, the Newton’s second law of classical dynamics, and the Maxwell field equations of the ...
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Stability of the Ricci flow at Ricci-flat metrics [PDF]
Communications in Analysis and Geometry, 2002 If \(g\) is a metric whose Ricci flow \(g(t)\) converges, one may ask if the same is true for metrics \(\widetilde g\) that are small perturbations of \(g\). The authors use maximal regularity theory and center manifold analysis to study flat and Ricci-flat metrics.
Christine Guenther +2 more
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Hyperbolic Gradient-Bourgoignon Flow
پژوهشهای ریاضی, 2022 Introduction Ricci solitons as a generalization of Einstein manifolds introduced by Hamilton in mid 1980s. In the last two decades, a lot of researchers have been done on Ricci solitons.
Hamed Faraji +2 more
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Ricci-Bourguignon flow on an open surface [PDF]
Journal of Mahani Mathematical Research, 2023 In this paper, we investigate the normalized Ricci-Bourguignon flow with incomplete initial metric on an open surface. We show that such a flow converges exponentially to a metric with constant Gaussian curvature if the initial metric is suitable.
Shahroud Azami
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Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2020 We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow smoothing techniques.
S. Huang, Xiaochun Rong, B. Wang
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A MECHANICS FOR THE RICCI FLOW
International Journal of Geometric Methods in Modern Physics, 2009 We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent Hamilton–Jacobi equation of the mechanics so defined.
P. Fernández de Córdoba +3 more
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SOME RESULTS ON ∗−RICCI FLOW [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2021 In this paper we have introduced the notion of ∗-Ricci flow and shown that ∗-Ricci soliton which was introduced by Kaimakamis and Panagiotidou in 2014 which is a self similar soliton of the ∗-Ricci flow. We have also find the deformation of geometric curvature tensors under ∗-Ricci flow.
Dipankar Debnath, Nirabhra Basu
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Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes
Journal of High Energy Physics, 2023 Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we consider the analog for the Einstein-Maxwell action, which gives Ricci flow with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell field.
Davide De Biasio +3 more
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