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A polyhedron comparison theorem for 3-manifolds with positive scalar curvature
Inventiones Mathematicae, 2017The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov.
Chao Li
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On the P-Scalar Curvature [PDF]
The Journal of Geometric Analysis, 2016 We study the P-scalar curvature operator used by Perelman in the context of manifolds with density. We verify that the Gromov–Lawson surgery for positive scalar curvature extends naturally to positive P-scalar curvature. By studying the first variation of the P-scalar curvature operator, we obtain local perturbation results for the P-scalar curvature ...
Farhan Abedin, Justin Corvino
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On generalized 4-th root metrics of isotropic scalar curvature
Mathematica Slovaca, 2018By an interesting physical perspective and a suitable contraction of the Riemannian curvature tensor in Finsler geometry, Akbar-Zadeh introduced the notion of scalar curvature for the Finsler metrics.
A. Tayebi
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1976
We shall deal with some problems concerning the scalar curvature of compact riemannian manifolds. In particular we shall deal with the problem of Yamabe: Does there exist a conformal metric for which the scalar curvature is constant? And also problems posed by Chern, Nirenberg and others.
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We shall deal with some problems concerning the scalar curvature of compact riemannian manifolds. In particular we shall deal with the problem of Yamabe: Does there exist a conformal metric for which the scalar curvature is constant? And also problems posed by Chern, Nirenberg and others.
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Sewing Riemannian Manifolds with Positive Scalar Curvature
Journal of Geometric Analysis, 2017We explore to what extent one may hope to preserve geometric properties of three-dimensional manifolds with lower scalar curvature bounds under Gromov–Hausdorff and Intrinsic Flat limits.
J. Basilio, J. Dodziuk, C. Sormani
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Total Mean Curvature, Scalar Curvature, and a Variational Analog of Brown–York Mass
, 2016We study the supremum of the total mean curvature on the boundary of compact, mean-convex 3-manifolds with nonnegative scalar curvature, and a prescribed boundary metric.
Christos Mantoulidis, P. Miao
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On the scalar curvature of compact hypersurfaces
Archiv der Mathematik, 1999In the paper under review, by using the method of integral formulas, the authors prove the following: Let \(M\) be a compact and connected hypersurface in the Euclidean space \(\mathbb{R} ^{n+1}\) with scalar curvature \(\tau\). If \(p^2 \tau \leq 1\), where \(p\) is the support function with respect to a point \(p _0\) in \(\mathbb{R} ^{n+1}\), then \(
S. L. Silva, Francisco Fontenele
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Annals of Global Analysis and Geometry, 1992
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Prescribed Scalar Curvature [PDF]
, 1998 Let (M n , g) be a C ∞ Riemannian manifold of dimension n ≥ 2. Given f a smooth function on M n , the Problem is: Does there exist a metric g′ on M such that the scalar curvature R′ of g′ is equal to f ?
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On positive scalar curvature on S 2
Calculus of Variations and Partial Differential Equations, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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