Results 1 to 10 of about 503,370 (190)
On scalar curvature lower bounds and scalar curvature measure [PDF]
Advances in Mathematics, 2021 John Lott
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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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dp–convergence and 𝜖–regularity theorems for entropy and scalar curvature lower bounds [PDF]
Geometry & Topology, 2020 Consider a sequence of Riemannian manifolds $(M^n_i,g_i)$ with scalar curvatures and entropies bounded below by small constants $R_i,\mu_i \geq-\epsilon_i$.
Man-Chun Lee, A. Naber, Robin Neumayer
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Rigidity results for complete manifolds with nonnegative scalar curvature [PDF]
Journal of differential geometry, 2020 In this paper, we are going to show some rigidity results for complete open Riemannian manifolds with nonnegative scalar curvature. Without using the famous Cheeger-Gromoll splitting theorem we give a new proof to a rigidity result for complete manifolds
Jintian Zhu
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Total mean curvature of the boundary and nonnegative scalar curvature fill-ins [PDF]
Journal für die Reine und Angewandte Mathematik, 2020 In the first part of this paper, we prove the extensibility of an arbitrary boundary metric to a positive scalar curvature (PSC) metric inside for a compact manifold with boundary, completely solving an open problem due to Gromov (see Question 1.1). Then
Yuguang Shi, Wenlong Wang, Guodong Wei
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Scalar and mean curvature comparison via the Dirac operator [PDF]
Geometry & Topology, 2021 We use the Dirac operator technique to establish sharp distance estimates for compact spin manifolds under lower bounds on the scalar curvature in the interior and on the mean curvature of the boundary.
Simone Cecchini, Rudolf Zeidler
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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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Quantitative K-theory, positive scalar curvature, and band width [PDF]
, 2020 We develop two connections between the quantitative framework of operator $K$-theory for geometric $C^*$-algebras and the problem of positive scalar curvature.
Haoyang Guo, Zhizhang Xie, Guoliang Yu
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Index theory for scalar curvature on manifolds with boundary [PDF]
, 2020 We extend results of Llarull and Goette-Semmelmann to manifolds with boundary.
J. Lott
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