Results 41 to 50 of about 406,237 (253)
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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On the Geometry of Three-dimensional Pseudo-Riemannian Homogeneous Spaces. II [PDF]
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, 2020 The problem of establishing links between the curvature and the topological structure of a manifold is one of the important problems of the geometry. In general, the purpose of the research of manifolds of various types is rather complicated.
Mozhey, Natal’ya Pavlovna
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The curvature of gradient Ricci solitons [PDF]
Mathematical Research Letters, 2011 We study integral and pointwise bounds on the curvature of gradient shrinking Ricci solitons. As applications we discuss gap and compactness results for gradient shrinkers.
Ovidiu Munteanu, Mu-Tao Wang
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On the Signature of the Ricci Curvature on Nilmanifolds [PDF]
Transformation Groups, 2022 11 ...
Arroyo, Romina M., Lafuente, Ramiro A.
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Graph Ricci curvatures reveal atypical functional connectivity in autism spectrum disorder
Scientific Reports, 2022 While standard graph-theoretic measures have been widely used to characterize atypical resting-state functional connectivity in autism spectrum disorder (ASD), geometry-inspired network measures have not been applied. In this study, we apply Forman–Ricci
Pavithra Elumalai +5 more
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Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry [PDF]
, 2005 We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups.
Gordina, Maria
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The Ricci curvature in noncommutative geometry [PDF]
Journal of Noncommutative Geometry, 2019 Motivated by the local formulae for asymptotic expansion of heat kernels in spectral geometry, we propose a definition of Ricci curvature in noncommutative settings. The Ricci operator of an oriented closed Riemannian manifold can be realized as a spectral functional, namely the functional defined by the zeta function of the full Laplacian of the de ...
Masoud Khalkhali +2 more
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A Note on the Geometry of RW Space-Times
Mathematics, 2023 A conformally flat GRW space-time is a perfect fluid RW space-time. In this note, we investigated the influence of many differential curvature conditions, such as the existence of recurrent and semi-symmetric curvature tensors.
Sameh Shenawy +2 more
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On the essential spectrum of complete non-compact manifolds [PDF]
, 2011 In this paper, we prove that the $L^p$ essential spectra of the Laplacian on functions are $[0,+\infty)$ on a non-compact complete Riemannian manifold with non-negative Ricci curvature at infinity.
Lu, Zhiqin, Zhou, Detang
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Non-collapsed spaces with Ricci curvature bounded from below [PDF]
, 2017 We propose a definition of non-collapsed space with Ricci curvature bounded from below and we prove the versions of Colding's volume convergence theorem and of Cheeger-Colding dimension gap estimate for ${\sf RCD}$ spaces. In particular this establishes
G. Philippis, N. Gigli
semanticscholar +1 more source