Results 41 to 50 of about 71,917 (238)
Mean curvature flow in a Ricci flow background
, 2012 Following work of Ecker, we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-with-boundary. We compute its variational properties and its time derivative under Perelman's modified Ricci flow.
B. Kleiner +14 more
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Matrix Inequality for the Laplace Equation
, 2017 Since Li and Yau obtained the gradient estimate for the heat equation, related estimates have been extensively studied. With additional curvature assumptions, matrix estimates that generalize such estimates have been discovered for various time-dependent
Park, Jiewon
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On Almost Nonpositive k-Ricci Curvature
The Journal of Geometric Analysis, 2022 Motivated by the recent work of Chu-Lee-Tam on the nefness of canonical line bundle for compact K hler manifolds with nonpositive $k$-Ricci curvature, we consider a natural notion of {\em almost nonpositive $k$-Ricci curvature}, which is weaker than the existence of a K hler metric with nonpositive $k$-Ricci curvature.
openaire +3 more sources
Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth Spaces [PDF]
, 2015 There are two primary goals to this paper. In the first part of the paper we study smooth metric measure spaces (M^n,g,e^{-f}dv_g) and give several ways of characterizing bounds -Kg\leq \Ric+\nabla^2f\leq Kg on the Ricci curvature of the manifold.
Naber, Aaron
core
Geometric realizations of generalized algebraic curvature operators
, 2008 We study the 8 natural GL equivariant geometric realization questions for the space of generalized algebraic curvature tensors. All but one of them is solvable; a non-zero projectively flat Ricci antisymmetric generalized algebraic curvature is not ...
Blažić N. +11 more
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Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs
Communications on Pure and Applied Mathematics, EarlyView.Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
wiley +1 more source
Ricci curvature of submanifolds in Kenmotsu space forms
International Journal of Mathematics and Mathematical Sciences, 2002 In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension.
Kadri Arslan +4 more
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Ricci curvatures on Hermitian manifolds
Transactions of the American Mathematical Society, 2017 In this paper, we introduce the first Aeppli-Chern class for complex manifolds and show that the ( 1 , 1 ) (1,1) -component of the curvature 2 2 -form of the Levi-Civita connection on the anti-canonical line bundle represents this class. We systematically investigate the relationship
Liu, Kefeng, Yang, Xiaokui
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Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons
Communications on Pure and Applied Mathematics, EarlyView.Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
wiley +1 more source
Ricci Curvature on Birth-Death Processes
Axioms, 2023 In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and Émery’s CD(K,n) condition for linear graphs and prove the triviality of edge weights for every linear graph ...
Bobo Hua, Florentin Münch
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