Results 21 to 30 of about 5,224,338 (238)
Pluripotential Kähler–Ricci flows [PDF]
Geometry & Topology, 2020 We develop a parabolic pluripotential theory on compact K{ä}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{è}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{ä}hler-Ricci flow on varieties with log terminal singularities.
Guedj, Vincent +2 more
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Yamabe constant evolution and monotonicity along the conformal Ricci flow
AIMS Mathematics, 2022 We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric $ g(t) $, $ t \in [0, T) $, the time evolution formula for the Yamabe constant $ Y(g(t)) $ is derived.
Yanlin Li +3 more
semanticscholar +1 more source
Communications in Mathematical Physics, 2014 We construct a discrete form of Hamilton's Ricci flow (RF) equations for a d-dimensional piecewise flat simplicial geometry, S. These new algebraic equations are derived using the discrete formulation of Einstein's theory of general relativity known as Regge calculus.
Miller, Warner A. +4 more
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The ∗-Ricci Operator on Hopf Real Hypersurfaces in the Complex Quadric
Mathematics, 2022 We study the ∗-Ricci operator on Hopf real hypersurfaces in the complex quadric. We prove that for Hopf real hypersurfaces in the complex quadric, the ∗-Ricci tensor is symmetric if and only if the unit normal vector field is singular.
Rongsheng Ma, Donghe Pei
doaj +1 more source
Uniqueness of compact ancient solutions to three-dimensional Ricci flow [PDF]
Inventiones Mathematicae, 2020 In this paper, we study the classification of κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin ...
S. Brendle, P. Daskalopoulos, N. Šešum
semanticscholar +1 more source
Algebraic uniqueness of Kähler–Ricci flow limits and optimal degenerations of Fano varieties [PDF]
Geometry & Topology, 2020 We prove that for any $\mathbb{Q}$-Fano variety $X$, the special $\mathbb{R}$-test configuration that minimizes the $H$-functional is unique and has a K-semistable $\mathbb{Q}$-Fano central fibre $(W, \xi)$.
Jiyuan Han, Chi Li
semanticscholar +1 more source
Evolution for First Eigenvalue of LT,f on an Evolving Riemannian Manifold
Mathematics, 2022 In this paper, evolution formulas for the first non-zero eigenvalue of the operator LT,f on a weighted closed Riemannian manifold along the Ricci flow as well as along the Yamabe flow are formulated.
Apurba Saha +4 more
doaj +1 more source
On the spectrum of the weighted p-Laplacian under the Ricci-harmonic flow
Journal of Inequalities and Applications, 2020 This paper studies the behaviour of the spectrum of the weighted p-Laplacian on a complete Riemannian manifold evolving by the Ricci-harmonic flow. Precisely, the first eigenvalue diverges in a finite time along this flow.
Abimbola Abolarinwa +2 more
doaj +1 more source
Pointwise lower scalar curvature bounds for $$C^0$$ metrics via regularizing Ricci flow [PDF]
Geometric and Functional Analysis, 2019 In this paper we propose a class of local definitions of weak lower scalar curvature bounds that is well defined for $$C^0$$ metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that ...
Paula Burkhardt-Guim
semanticscholar +1 more source
Ricci Flow and Ricci Limit Spaces [PDF]
, 2020 I survey some of the developments in the theory of Ricci flow and its applications from the past decade. I focus mainly on the understanding of Ricci flows that are permitted to have unbounded curvature in the sense that the curvature can blow up as we wander off to spatial infinity and/or as we decrease time to some singular time.
openaire +2 more sources