Results 51 to 60 of about 727 (144)
Communications in Mathematical Physics, 2007 In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show that the mass is invariant under the flow in dimension three (similar results hold in higher dimension with more assumptions).
Dai, Xianzhe, Ma, Li
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On classification of degenerate singular points of Ricci flows
Қарағанды университетінің хабаршысы. Математика сериясы, 2015 We consider the normalized Ricci flow on generalized Wallach spaces that could be reduced to a system of nonlinear ODEs. As a main result we get the classification of degenerate singular points of the system under consideration in the important partial ...
N.А. Аbiev
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Pluripotential Chern-Ricci flows
Indiana University Mathematics JournalExtending a recent theory developed on compact Kähler manifolds by Guedj-Lu-Zeriahi and the author, we define and study pluripotential solutions to degenerate parabolic complex Monge-Ampère equations on compact Hermitian manifolds. Under natural assumptions on the Cauchy boundary data, we show that the pluripotential solution is semi-concave in time ...
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Regularising the Ricci Flow Embedding [PDF]
, 2010 This paper concerns the analysis of patterns that are specified in terms of non-Euclidean dissimilarity or proximity rather than ordinal values. In prior work we have reported a means of correcting or rectifying the similarities so that the non-Euclidean artifacts are minimized.
Xu W., Hancock E.R., Wilson R.C.
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Recent Developments in Ricci Flows
Notices of the American Mathematical Society, 2021 This is a survey on recent developments in Ricci flows.
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Combinatorial Ricci Flows on Surfaces
Journal of Differential Geometry, 2003 We show that the analog of Hamilton's Ricci flow in the combinatorial setting produces solutions which converge exponentially fast to Thurston's circle packing on surfaces. As a consequence, a new proof of Thurston's existence of circle packing theorem is obtained. As another consequence, Ricci flow suggests a new algorithm to find circle packings.
Chow, Bennett, Luo, Feng
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A note on the Cotton flow and the Ricci flow for three-manifolds, and the Hořava–Lifshitz gravity
European Physical Journal C: Particles and FieldsWe consider the more general geometrical flow in the space of metrics for three-manifolds that consists of a combination of two flows, the Cotton flow and the Ricci flow; by playing a fundamental role in the detailed balance principle of the four ...
R. Cartas-Fuentevilla +2 more
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A local singularity analysis for the Ricci flow and its applications to Ricci flows with bounded scalar curvature. [PDF]
Calc Var Partial Differ Equ, 2022 Buzano R, Di Matteo G.
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European Physical Journal C: Particles and FieldsWe extend the anholonomic frame and connection deformation method, AFCDM, for constructing exact and parametric solutions in general relativity, GR, to geometric flow models and modified gravity theories, MGTs, with nontrivial torsion and nonmetricity ...
Laurenţiu Bubuianu +3 more
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Singularities of Connection Ricci Flow and Ricci Harmonic Flow
, 2013 In this paper, we study the singularities of two extended Ricci flow systems --- connection Ricci flow and Ricci harmonic flow using newly-defined curvature quantities. Specifically, we give the definition of three types of singularities and their corresponding singularity models, and then prove the convergence. In addition, for Ricci harmonic flow, we
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