Results 11 to 20 of about 685,590 (201)
Translation hypersurfaces of semi-Euclidean spaces with constant scalar curvature
AIMS Mathematics, 2023 In this paper, we present translation hypersurfaces of semi-Euclidean spaces with zero scalar curvature. In addition, we prove that translation hypersurfaces with constant scalar curvature must have zero scalar curvature in the semi-Euclidean space ...
Derya Sağlam, Cumali Sunar
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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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On the constant scalar curvature Kähler metrics (II)—Existence results
Journal of The American Mathematical Society, 2020 In this paper, we apply our previous estimates in Chen and Cheng [On the constant scalar curvature Kähler metrics (I): a priori estimates, Preprint] to study the existence of cscK metrics on compact Kähler manifolds. First we prove that the properness of
Xiuxiong Chen, Jingrui Cheng
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Horizon curvature and spacetime structure influences on black hole scalarization
European Physical Journal C: Particles and Fields, 2021 Black hole spontaneous scalarization has been attracting more and more attention as it circumvents the well-known no-hair theorems. In this work, we study the scalarization in Einstein–scalar-Gauss–Bonnet theory with a probe scalar field in a black hole ...
Hong Guo +3 more
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Scalar curvature and harmonic maps to $S^1$ [PDF]
Journal of differential geometry, 2019 For a harmonic map $u:M^3\to S^1$ on a closed, oriented $3$--manifold, we establish the identity $$2\pi \int_{\theta\in S^1}\chi(\Sigma_{\theta})\geq \frac{1}{2}\int_{\theta\in S^1}\int_{\Sigma_{\theta}}(|du|^{-2}|Hess(u)|^2+R_M)$$ relating the scalar ...
Daniel Stern
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Positive scalar curvature and minimal hypersurface singularities [PDF]
Surveys in Differential Geometry, 2017 In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption.
R. Schoen, S. Yau
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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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Constrained deformations of positive scalar curvature metrics [PDF]
Journal of differential geometry, 2019 We present a series of results concerning the interplay between the scalar curvature of a manifold and the mean curvature of its boundary. In particular, we give a complete topological characterization of those compact 3-manifolds that support Riemannian
A. Carlotto, Chao Li
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A rigidity theorem for nonvacuum initial data [PDF]
, 2001 In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature.
Choquet-Bruhat Y. +10 more
core +4 more sources