Results 51 to 60 of about 4,696,479 (281)
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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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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An Introduction to the Kähler-Ricci Flow [PDF]
, 2013 This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kähler-Ricci flow and its current state-of-the-art. While several excellent books on Kähler-Einstein geometry are available, there have been no such works on the Kähler-Ricci flow.
Boucksom, Sébastien +2 more
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On the stability of harmonic maps under the homogeneous Ricci flow
Complex Manifolds, 2018 In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow.We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow does not ...
Prado Rafaela F. do, Grama Lino
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RICCI LOWER BOUND FOR KÄHLER–RICCI FLOW [PDF]
Communications in Contemporary Mathematics, 2014 We provide general discussion on the lower bound of Ricci curvature along Kähler–Ricci flows over closed manifolds. The main result is the non-existence of Ricci lower bound for flows with finite time singularities and non-collapsed global volume. As an application, we give examples showing that positivity of Ricci curvature would not be preserved by ...
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Characterizations of Trivial Ricci Solitons
Advances in Mathematical Physics, 2020 Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton.
Sharief Deshmukh +2 more
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Ricci Soliton and Certain Related Metrics on a Three-Dimensional Trans-Sasakian Manifold
Universe, 2022 In this article, a Ricci soliton and *-conformal Ricci soliton are examined in the framework of trans-Sasakian three-manifold. In the beginning of the paper, it is shown that a three-dimensional trans-Sasakian manifold of type (α,β) admits a Ricci ...
Zhizhi Chen +4 more
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Communications on Pure and Applied Mathematics, 2012 AbstractIn this paper, we study the moduli spaces of m‐dimensional, κ‐noncollapsed Ricci flow solutions with bounded $\int |Rm|^{{m}/{2}}$ and bounded scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study the estimates of isoperimetric constants, the Kähler‐Ricci flows, and the moduli spaces of gradient ...
Chen, Xiuxiong, Wang, Bing
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Stability of Kähler-Ricci Flow [PDF]
Journal of Geometric Analysis, 2009 We prove the convergence of K hler-Ricci flow with some small initial curvature conditions. As applications, we discuss the convergence of K hler-Ricci flow when the complex structure varies on a K hler-Einstein manifold.
Chen, Xiuxiong, Li, Haozhao
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Ricci Solitons and Einstein-Scalar Field Theory
, 2009 B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism.
Anderson M T +20 more
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