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Ricci flow coupled with harmonic map flow [PDF]
, 2012 07.02.13 KB. Accepted version ok to add to Spiral. SMF/SherpaWe investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N ...
Reto Müller, Müller, Reto, Müller, R
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International Journal of Mathematics and Mathematical Sciences, 2010 We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound, and apply it to investigate the volume growth, total Betti number, and finite topological type of ...
Zisheng Hu, Yadong Jin, Senlin Xu
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On generalized complex space forms satisfying certain curvature conditions
Karpatsʹkì Matematičnì Publìkacìï, 2016 We study Ricci soliton $(g,V,\lambda)$ of generalized complex space forms when the Riemannian, Bochner and $W_{2}$ curvature tensors satisfy certain curvature conditions like semi-symmetric, Einstein semi-symmetric, Ricci pseudo symmetric and Ricci ...
M.M. Praveena, C.S. Bagewadi
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Ricci curvature and betti numbers [PDF]
Journal of Geometric Analysis, 1997 18pages ...
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L-optimal transportation for Ricci flow [PDF]
, 2009 We introduce the notion of L-optimal transportation, and use it to construct a natural monotonic quantity for Ricci flow which includes a selection of other monotonicity results, including some key discoveries of Perelman [13] (both related to entropy ...
Topping, Peter
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Boundary effect of Ricci curvature [PDF]
Journal of Differential Geometry, 2016 On a compact Riemannian manifold with boundary, we study how Ricci curvature of the interior affects the geometry of the boundary. First we establish integral inequalities for functions defined solely on the boundary and apply them to obtain geometric inequalities involving the total mean curvature.
Miao, Pengzi, Wang, Xiaodong
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Ricci Curvature, Isoperimetry and a Non-additive Entropy
Entropy, 2015 Searching for the dynamical foundations of Havrda-Charvát/Daróczy/ Cressie-Read/Tsallis non-additive entropy, we come across a covariant quantity called, alternatively, a generalized Ricci curvature, an N-Ricci curvature or a Bakry-Émery-Ricci curvature ...
Nikos Kalogeropoulos
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Ricci curvature and volume growth [PDF]
Pacific Journal of Mathematics, 1991 The well known Bishop-Gromov inequality for the volume growth of balls in a Riemannian manifold \(M\) has an analogue for tubes around a compact totally geodesic submanifold \(L\subset M\), but instead of a lower Ricci curvature bound one has to assume a lower bound \(\kappa\) for the radial sectional curvatures of \(M\) with respect to \(L\).
Strake, M., Walschap, G.
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Estimates on the non-compact expanding gradient Ricci solitons
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mn,g) with positive Ricci curvature. On the condition that the Ricci curvature is positive and the scalar curvature approaches 0 towards infinity, we derive a useful ...
Gao Xiang, Xing Qiaofang, Cao Rongrong
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Ricci Curvature on Polyhedral Surfaces via Optimal Transportation
Axioms, 2014 The problem of correctly defining geometric objects, such as the curvature, is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs.
Benoît Loisel, Pascal Romon
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