Ricci Curvature
Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
... If K > 0 and N 2 N , by the Lévy–Gromov isoperimetric inequality we know that, for N–dimensional smooth manifolds having Ricci curvature bounded below by K , the Cheeger constant i is bounded below by ...
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Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound
... The purpose of this paper is three-fold. First, we revisit classical lower bounds for Laplace eigenvalues on closed Riemannian manifolds due to Gromov and Buser, and give an alternative unified approach to these ...
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On quotients of spaces with Ricci curvature bounded below
... sectional curvature of (M, g) is again a bound for the curvature of the quotient space, which is an Alexandrov space of curvature bounded ...synthetic Ricci curvature lower ...weighted ...
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Hypersurfaces with nonnegative Ricci curvature in hyperbolic space
... to Ricci curvature are sometimes reduced to the n-Laplacian ...nonnegative Ricci curvature give rise to height functions that are Euclidean ...nonnegative Ricci curvature must ...
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Manifolds with Bakry Emery Ricci Curvature Bounded Below
... Émery Ricci curvature bounded below and with bounded potential function then M is ...Bakry-Émery Ricci curvature which allows us to prove a topolological rigidity theorem for such ...
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On the structure of Riemannian manifolds of almost nonnegative Ricci curvature
... Ricci curvature. We prove a compact Riemannian manifold with bounded curvature, diameter bounded from above, and Ricci curvature bounded from below by an almost nonnegative real number ...
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Ricci curvature of submanifolds in Kenmotsu space forms
... the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary ...the Ricci curvature and the squared mean curvature for ...
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Ricci Curvature of Noncommutative Three Tori, Entropy, and Second Quantization
... scalar curvature, and Ricci ...the Ricci curvature from the asymptotic expansion of the heat trace Tr(e −tD 2 ...the Ricci curvature of a curved noncommutative three ...
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Almost euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds
... satisfying Ricci curvature lower bounds in a synthetic sense are the so called RCD ∗ (K, N )-spaces, which include the notable subclasses of Alexandrov spaces with curvature bounded below (see [30]), ...
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Sectional and intermediate Ricci curvature lower bounds via optimal transport
... p-Ricci curvature in terms of optimal transport, for any p ∈ {1, ...p-Ricci curvature we refer to Section 2, here let us just mention the intuitive idea behind: in the standard Ricci ...
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Sharp and rigid isoperimetric inequalities in metric measure spaces with lower Ricci curvature bounds
... sense) Ricci curvature bounded from below by K > 0 and dimension bounded above by N ∈ [1,∞), then the classic L´ evy-Gromov isoperimetric inequality (together with the recent sharpening counterparts ...
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Inequality for Ricci curvature of certain submanifolds in locally conformal almost cosymplectic manifolds
... Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for submanifolds in real space forms (see [4]). We prove similar inequalities for slant, bi-slant, and ...
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A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications
... symmetric Ricci curvature lower bound,k at the point p if there exists a continuous function k : 0, l → R such that, for any tangent vector v ∈ T x M radial from the point ...
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Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds
... Abstract. We prove that the results regarding the Isoperimetric inequality and Cheeger constant formulated in terms of the Minkowski content, obtained by the authors in previous papers [15, 16] in the framework of ...
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Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds
... As a particular case of the property (ii) ′ above, we see that the conformal minimal vol- ume of any finite volume quotient G \ Γ vanishes. In addition to the properties in Lemma 4.3, it is harmless to assume that for ...
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The CPT-RICCI Scalar Curvature Symmetry in Quantum Electro-Gravity
... the Ricci curvature in passing from matter to antimatter and that the CPT transformation, associated to the reversing of the trace of the Ricci curvature, leads to a more general symmetry in ...
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On the Existence of Spacetime Structure
... or ontological issues. One of the regions, that with stress-energy, has non-trivial Ricci curvature; the other does not, though it may have non-trivial Weyl curvature. That difference by[r] ...
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On Chen invariants and inequalities in quaternionic geometry
... of Ricci curvature to k-Ricci curvature for a Rieman- nian manifold and established a sharp relationship between k-Ricci curvatures and the shape operator and also a sharp relationship ...
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3.Sobolev-type inequalities and complete Riemannian manifolds with nonnegative Ricci curvature
... 3.3. Heat kernel asymptotics. Ledoux [16] proposed that a nonnegatively Ricci curved n-dimensional Riemannian manifold M is isometric to R n if M satisfies the Nash ineqaulity (1.7) with optimal constant (1.11). ...
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Ricci Flow On Cohomogeneity One Manifolds
... the Ricci flow is a nonlinear and degenerate parabolic PDE, which makes its analysis very ...the Ricci flow has been used to prove a number of remarkable theorems in geometry and ...positive Ricci ...
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