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On Gauss-Bonnet Curvatures [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 The $(2k)$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k)$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k = 1$.
Mohammed Larbi Labbi
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Mean curvature flow with convex Gauss image [PDF]
Chinese Annals of Mathematics Series B, 2008 36 ...
Yuanlong Xin, Xin Yuanlong
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Prescription of Gauss curvature on compact hyperbolic orbifolds [PDF]
Discrete and Continuous Dynamical Systems, 2014 This paper is organized in the following way: Section 1 contains preliminaries and the problem of prescribing the Gauss curvature of convex sets in the Minkowski spacetime, which is a generalization of a result by Alexandrov for Euclidean convex bodies.
Jérôme Bertrand
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Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure
Advanced Nonlinear Studies, 2023 In this article, we study the Musielak-Orlicz-Gauss image problem based on the Gauss curvature flow in Li et al. We deal with some cases in which there is no uniform estimate for the Gauss curvature flow.
Li Qi-Rui, Yi Caihong
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Conflict between some higher-order curvature invariant terms
Nuclear Physics B, 2021 A viable quantum theory does not allow curvature invariant terms of different higher orders to be accommodated in the gravitational action. We show that there is indeed a conflict between the curvature squared and Gauss-Bonnet squared terms from the ...
Dalia Saha +3 more
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Spheres and Tori as Elliptic Linear Weingarten Surfaces
Mathematics, 2022 The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric.
Dong-Soo Kim, Young Ho Kim, Jinhua Qian
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Inverse Gauss Curvature Flows and Orlicz Minkowski Problem
Analysis and Geometry in Metric Spaces, 2022 Liu and Lu [27] investigated a generalized Gauss curvature flow and obtained an even solution to the dual Orlicz-Minkowski problem under some appropriate assumptions.
Chen Bin, Cui Jingshi, Zhao Peibiao
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Remarks on prescribing Gauss curvature [PDF]
Transactions of the American Mathematical Society, 1993 We study the nonlinear partial differential equation for the problem of prescribing Gauss curvature K K on
Xu, Xingwang, Yang, Paul C.
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A Note on Superspirals of Confluent Type
Mathematics, 2020 Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function.
Jun-ichi Inoguchi +2 more
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Hypersurfaces with pointwise 1-type Gauss map in Lorentz–Minkowski space; 146–161 [PDF]
Proceedings of the Estonian Academy of Sciences, 2009 Hypersurfaces of a LorentzâMinkowski space Ln+1 with pointwise 1-type Gauss map are characterized. We prove that an oriented hypersurface Mq in Ln+1 has pointwise 1-type Gauss map of the first kind if and only if Mq has constant mean curvature and ...
Uğur Dursun
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