Results 1 to 10 of about 681,612 (344)
On scalar curvature lower bounds and scalar curvature measure [PDF]
Advances in Mathematics, 2021 We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a Ricci flow solution.
J. Lott
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Boundary Conditions for Scalar Curvature [PDF]
, 2020 Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a general deformation
Christian Baer, B. Hanke
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Scalar curvature in discrete gravity
European Physical Journal C: Particles and Fields, 2022 We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings.
Ali H. Chamseddine +2 more
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A Splitting Theorem for Scalar Curvature [PDF]
Communications on Pure and Applied Mathematics, 2018 We show that a Riemannian 3‐manifold with nonnegative scalar curvature is flat if it contains an area‐minimizing cylinder. This scalar‐curvature analogue of the classical splitting theorem of J. Cheeger and D. Gromoll (1971) was conjectured by D. Fischer‐
Otis Chodosh, M. Eichmair, Vlad Moraru
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Mean Curvature in the Light of Scalar Curvature [PDF]
Annales de l'Institut Fourier, 2018 We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
M. Gromov
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O(p + 1) x O(p + 1)-Invariant hypersurfaces with zero scalar curvature in euclidean space [PDF]
Anais da Academia Brasileira de Ciências, 2000 We use equivariant geometry methods to study and classify zero scalar curvature O(p + 1) x O(p + 1)-invariant hypersurfaces in R2p+2 with p > 1.
JOCELINO SATO
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Metric Inequalities with Scalar Curvature [PDF]
Geometric and Functional Analysis, 2017 We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is concerned these inequalities appear as generalisations of the classical bounds on ...
M. Gromov
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Scalar curvature and singular metrics [PDF]
Pacific Journal of Mathematics, 2016 Let $M^n$, $n\ge3$, be a compact differentiable manifold with nonpositive Yamabe invariant $\sigma(M)$. Suppose $g_0$ is a continuous metric with $V(M, g_0)=1$, smooth outside a compact set $\Sigma$, and is in $W^{1,p}_{loc}$ for some $p>n$.
Yuguang Shi, Luen-Fai Tam
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Geometry of positive scalar curvature on complete manifold [PDF]
Journal für die Reine und Angewandte Mathematik, 2022 In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature.
Bo Zhu
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Weak scalar curvature lower bounds along Ricci flow [PDF]
Science China Mathematics, 2021 In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon (2002) that the Ricci flow exists for a short time.
Wenshuai Jiang +2 more
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