Results 71 to 80 of about 13,435 (197)
A positive mass theorem for two spatial dimensions [PDF]
, 2012 We observe that an analogue of the Positive Mass Theorem in the time-symmetric case for three-space-time-dimensional general relativity follows trivially from the Gauss-Bonnet theorem. In this case we also have that the spatial slice is diffeomorphic to $
Wong, Willie Wai-Yeung
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Curvature varifolds with orthogonal boundary
Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.Abstract We consider the class S⊥m(Ω)${\bf S}^m_\perp (\Omega)$ of m$m$‐dimensional surfaces in Ω¯⊂Rn$\overline{\Omega } \subset {\mathbb {R}}^n$ that intersect S=∂Ω$S = \partial \Omega$ orthogonally along the boundary. A piece of an affine m$m$‐plane in S⊥m(Ω)${\bf S}^m_\perp (\Omega)$ is called an orthogonal slice.
Ernst Kuwert, Marius Müller
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Applications of the Gauss-Bonnet theorem to gravitational lensing
, 2008 In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit.
Binney J +8 more
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Hyperbolicity in non‐metric cubical small‐cancellation
Bulletin of the London Mathematical Society, Volume 56, Issue 6, Page 2036-2052, June 2024.Abstract Given a non‐positively curved cube complex X$X$, we prove that the quotient of π1X$\pi _1X$ defined by a cubical presentation ⟨X∣Y1,⋯,Ys⟩$\langle X\mid Y_1,\dots, Y_s\rangle$ satisfying sufficient non‐metric cubical small‐cancellation conditions is hyperbolic provided that π1X$\pi _1X$ is hyperbolic.
Macarena Arenas +2 more
wiley +1 more source
MathematicsThe aim of this paper is to obtain the sub-Riemannian properties of the roto-translation group RT. At the same time, we compute the sub-Riemannian limits of Gaussian curvature associated with two kinds of canonical connections for a C2-smooth surface in ...
Han Zhang, Haiming Liu
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Holographic aspects of a higher curvature massive gravity
European Physical Journal C: Particles and Fields, 2019 We study the holographic dual of a massive gravity with Gauss–Bonnet and cubic quasi-topological higher curvature terms. Firstly, we find the energy–momentum two point function of the 4-dimensional boundary theory where the massive term breaks the ...
Shahrokh Parvizi, Mehdi Sadeghi
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Indian Journal of Pure and Applied Mathematics, 2015 In this note we give a proof of the Gauss-Bonnet theorem for Riemannian manifolds (of any dimension) using Morse theory.
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Uniqueness of Ricci flows from non‐atomic Radon measures on Riemann surfaces
Proceedings of the London Mathematical Society, Volume 128, Issue 6, June 2024.Abstract In previous work (Topping and Yin, https://arxiv.org/abs/2107.14686), we established the existence of a Ricci flow starting with a Riemann surface coupled with a non‐atomic Radon measure as a conformal factor. In this paper, we prove uniqueness, settling Conjecture 1.3 of Topping and Yin (https://arxiv.org/abs/2107.14686).
Peter M. Topping, Hao Yin
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New anisotropic Gauss–Bonnet black holes in five dimensions at the critical point
European Physical Journal C: Particles and FieldsWe obtain new vacuum static black hole solutions with anisotropic horizons in Einstein–Gauss–Bonnet gravity with a negative cosmological constant in five dimensions.
Yuxuan Peng
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The Gauss-Bonnet-Chern theorem: A probabilistic perspective [PDF]
Transactions of the American Mathematical Society, 2016 35 pages, references added, fixed typos, to appear Trans. Amer.
Nicolaescu, Liviu I., Savale, Nikhil
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