Results 11 to 20 of about 74,327 (228)
Asymptotically safe f(R)-gravity coupled to matter II: Global solutions [PDF]
Physics Letters B, 2019 Ultraviolet fixed point functions of the functional renormalisation group equation for f(R)-gravity coupled to matter fields are discussed. The metric is split via the exponential parameterisation into a background metric and a fluctuating part, the ...
Natália Alkofer
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Stability of quadratic curvature functionals at product of Einstein manifolds [PDF]
Proceedings - Mathematical Sciences, 2021 In this paper, we study Riemannian functionals defined by $L^2$-norms of Ricci curvature, scalar curvature, Weyl curvature, and Riemannian curvature. We try to understand stability of their critical points that are products of Einstein metrics. In particular, we prove that the product of a spherical space form and a compact hyperbolic manifold is ...
Bhattacharya, Atreyee, Maity, Soma
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An approach to quantum 2D gravity
Physics Letters B, 2023 We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as integrals over the SL(2,R) invariant Gaussian functional measure.
Vladimir V. Belokurov +1 more
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Rigidity of critical metrics for quadratic curvature functionals
Journal de Mathématiques Pures et Appliquées, 2023 In this paper we prove new rigidity results for complete, possibly non-compact, critical metrics of the quadratic curvature functionals $\mathfrak{F}^{2}_t = \int |\operatorname{Ric}_g|^{2} dV_g + t \int R^{2}_g dV_g$, $t\in\mathbb{R}$, and $\mathfrak{S}^2 = \int R_g^{2} dV_g$. We show that (i) flat surfaces are the only critical points of $\mathfrak{S}
Catino, Giovanni +2 more
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Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds [PDF]
Colloquium Mathematicum, 2022 Summary: We study rigidity of critical metrics for quadratic curvature functions \(\mathcal{F}_{t,s}(g)\) involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor. In particular, when \(s=0\), we give new characterizations by pointwise inequalities involving the Weyl curvature and the traceless Ricci tensor for critical ...
Ma, Bingqing, Huang, Guangyue
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Variational properties of quadratic curvature functionals [PDF]
Science China Mathematics, 2018 Accepted by SCIENCE CHINA Mathematics.
Sheng, Weimin, Wang, Lisheng
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Rigidity of Einstein Metrics as Critical Points of Some Quadratic Curvature Functionals on Complete Manifolds [PDF]
The Journal of Geometric Analysis, 2021 In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide rigidity results by the integral inequalities involving the Weyl curvature, the trace-less Ricci curvature and the ...
Huang, Guangyue, Chen, Yu, Li, Xingxiao
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Differential Patterns of Gyral and Sulcal Morphological Changes During Normal Aging Process
Frontiers in Aging Neuroscience, 2021 The cerebral cortex is a highly convoluted structure with distinct morphologic features, namely the gyri and sulci, which are associated with the functional segregation or integration in the human brain.
Hsin-Yu Lin +12 more
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Critical metrics for quadratic curvature functionals on some solvmanifolds
Revista Matemática Complutense, 2023 AbstractWe prove the existence of four-dimensional compact manifolds admitting some non-Einstein Lorentzian metrics, which are critical points for all quadratic curvature functionals. For this purpose, we consider left-invariant semi-direct extensions $$G_{\mathcal S}=H \rtimes \exp ({\mathbb {R}}S)$$
Giovanni Calvaruso, Amirhesam Zaeim
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Holographic entanglement entropy for perturbative higher-curvature gravities
Journal of High Energy Physics, 2021 The holographic entanglement entropy functional for higher-curvature gravities involves a weighted sum whose evaluation, beyond quadratic order, requires a complicated theory-dependent splitting of the Riemann tensor components.
Pablo Bueno +2 more
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