The Soliton-Ricci Flow with variable volume forms
Complex Manifolds, 2016 We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the ...
Pali Nefton
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Pluripotential Kähler–Ricci flows [PDF]
Geometry & Topology, 2020 We develop a parabolic pluripotential theory on compact K{ }hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{ }re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{ }hler-Ricci flow on varieties with log terminal singularities.
Vincent Guedj +2 more
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Hyperbolic Kahler-Ricci Flow [PDF]
Science China Mathematics, 2009 19 ...
Chao Xu
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Non-local interaction in discrete Ricci curvature-induced biological aggregation [PDF]
Royal Society Open ScienceWe investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods.
Jyotiranjan Beuria, Laxmidhar Behera
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Scalar Curvature, Entropy, and Generalized Ricci Flow [PDF]
International mathematics research notices, 2022 We derive a family of weighted scalar curvature monotonicity formulas for generalized Ricci flow, involving an auxiliary dilaton field evolving by a certain reaction–diffusion equation motivated by renormalization group flow.
J. Streets
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On finite time Type I singularities of the Kähler–Ricci flow on compact Kähler surfaces [PDF]
Journal of the European Mathematical Society (Print), 2022 We show that the underlying complex manifold of a complete non-compact two-\linebreak dimensional shrinking gradient K\"ahler-Ricci soliton $(M,\,g,\,X)$ with soliton metric $g$ with bounded scalar curvature $\operatorname{R}_{g}$ whose soliton vector ...
C. Cifarelli +2 more
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Parabolic Frequency Monotonicity on Ricci Flow and Ricci-Harmonic Flow with Bounded Curvatures [PDF]
Journal of Geometric Analysis, 2022 In this paper, we study the monotonicity of parabolic frequency motivated by Baldauf and Kim (Parabolic frequency on Ricci flows. To appear in Int. Math. Res. Not., rnac128.
C. Li, Yi Li, Kairui Xu
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Radiometric Constraints on the Timing, Tempo, and Effects of Large Igneous Province Emplacement
Geophysical Monograph Series, Page 27-82., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Jennifer Kasbohm +2 more
wiley +4 more sources
Weak scalar curvature lower bounds along Ricci flow [PDF]
Science China Mathematics, 2021 In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon (2002) that the Ricci flow exists for a short time.
Wenshuai Jiang +2 more
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Uniqueness of compact ancient solutions to the higher-dimensional Ricci flow [PDF]
Journal für die Reine und Angewandte Mathematik, 2021 In dimensions n ≥ 4 {n\geq 4} , an ancient κ-solution is a nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is κ-noncollapsed.
S. Brendle +3 more
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