Results 31 to 40 of about 2,543 (168)
Surfaces with prescribed Gauss curvature
Duke Mathematical Journal, 2000 This paper is concerned with prescribing Gaussian curvature for surfaces over \(\mathbb{R}^2\), i.e. with discussing existence and uniqueness for the following semilinear elliptic PDE: \[ K(x)=-e ^{-2u(x)}\Delta u(x) \] in the unknown function \(u\). The authors adopt a new approach to this long standing problem, which permit them to consider a wide ...
Chanillo, Sagun, Kiessling, Michael
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Lorentzian Approximations and Gauss–Bonnet Theorem for E1,1 with the Second Lorentzian Metric
Journal of Mathematics, 2022 In this paper, we consider the Lorentzian approximations of rigid motions of the Minkowski plane EL21,1. By using the method of Lorentzian approximations, we define the notions of the intrinsic curvature for regular curves, the intrinsic geodesic ...
Haiming Liu, Xiawei Chen
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Holographic p-wave superfluid in Gauss–Bonnet gravity
Physics Letters B, 2017 We construct the holographic p-wave superfluid in Gauss–Bonnet gravity via a Maxwell complex vector field model and investigate the effect of the curvature correction on the superfluid phase transition in the probe limit.
Shancheng Liu, Qiyuan Pan, Jiliang Jing
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Special Curves in Engineering. Surfaces Generated by the Logarithmic Spiral
Modelling in Civil Environmental Engineering, 2022 The logarithmic spiral is one of the most known curves with applications in engineering. We consider product of the logarithmic spiral with a real line and tensor product of two logarithmic spirals and investigate their minimality or flatness.
Broscăţeanu Ștefan Cezar
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On hyperbolic Gauss curvature flows
Journal of Differential Geometry, 2011 Contrast to the hyperbolic mean curvature flows studied in "Hyperbolic mean curvature flow," J. Differential Equations 246 (2009), 373–390, "The hyperbolic mean curvature flow," J. Math. Pures Appl. 90 (2008) 591–614, and "Formation of singularities in the motion of plane curves under hyperbolic mean curvature flow," J. Differential Equations 247 (2009)
Chou, Kai-Seng, Wo, Weifeng
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Journal of Mathematics, 2021 The rototranslation group ℛT is the group comprising rotations and translations of the Euclidean plane which is a 3-dimensional Lie group. In this paper, we use the Riemannian approximation scheme to compute sub-Riemannian limits of the Gaussian ...
Haiming Liu +3 more
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Gauss curvature flow with shrinking obstacle
Mathematische Annalen, 2023 We consider a flow by powers of Gauss curvature under the obstruction that the flow cannot penetrate a prescribed region, so called an obstacle. For all dimensions and positive powers, we prove the optimal curvature bounds of solutions and all time existence with its long time behavior.
Ki-Ahm Lee, Taehun Lee
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Scalar field collapse in Gauss–Bonnet gravity
European Physical Journal C: Particles and Fields, 2018 We consider a “scalar-Einstein–Gauss–Bonnet” theory in four dimension, where the scalar field couples non-minimally with the Gauss–Bonnet (GB) term. This coupling with the scalar field ensures the non-topological character of the GB term.
Narayan Banerjee, Tanmoy Paul
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Sub-Lorentzian Geometry of Curves and Surfaces in a Lorentzian Lie Group
Advances in Mathematical Physics, 2022 We consider the sub-Lorentzian geometry of curves and surfaces in the Lie group E1,1. Firstly, as an application of Riemannian approximants scheme, we give the definition of Lorentzian approximants scheme for E1,1 which is a sequence of Lorentzian ...
Haiming Liu, Jianyun Guan
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Binormal Motion of Curves with Constant Torsion in 3-Spaces
Advances in Mathematical Physics, 2017 We study curve motion by the binormal flow with curvature and torsion depending velocity and sweeping out immersed surfaces. Using the Gauss-Codazzi equations, we obtain filaments evolving with constant torsion which arise from extremal curves of ...
Josu Arroyo +2 more
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