Results 61 to 70 of about 2,543 (168)
Motion of hypersurfaces by Gauss curvature [PDF]
Pacific Journal of Mathematics, 2000 Let \(\Omega_0\) be a bounded convex region in \(\mathbb{R}^{n+1}\) with smooth boundary \(M_0= \partial\Omega_0\). We denote by \(K\) the Gauss curvature of a hypersurface \(M\) in \(\mathbb{R}^{n+1}\) with the outward normal vector \(\nu\) for \(M\).
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Magnetic brane solutions in Gauss–Bonnet–Maxwell massive gravity
Physics Letters B, 2017 Magnetic branes of Gauss–Bonnet–Maxwell theory in the context of massive gravity is studied in detail. Exact solutions are obtained and their interesting geometrical properties are investigated.
Seyed Hossein Hendi +3 more
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$\alpha$-Gauss Curvature flows
, 2013 In this paper, we study the deformation of the n-dimensional strictly convex hypersurface in $\mathbb R^{n+1}$ whose speed at a point on the hypersurface is proportional to $\alpha$-power of positive part of Gauss Curvature. For $\frac{1}{n}
Kim, Lami, Lee, Ki-ahm
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The capillary Gauss curvature flow
In this article, we first introduce a Gauss curvature type flow for capillary hypersurfaces, which we call capillary Gauss curvature flow. We then show that the flow will shrink to a point in finite time. This is a capillary counterpart (or Robin boundary counterpart) of Firey's problem studied in [Mathematika 21 (1974), pp. 1-11] and Tso [Comm.
Mei, Xinqun +2 more
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Prescription of Gauss curvature on compact hyperbolic orbifolds [PDF]
Discrete & Continuous Dynamical Systems - A, 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.
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Exterior Dirichlet Problem for Translating Solutions of Gauss Curvature Flow in Minkowski Space
Abstract and Applied Analysis, 2014 We prove the existence of solutions to a class of Monge-Ampère equations on exterior domains in ℝn(n≥2) and the solutions are close to a cone. This problem comes from the study of the flow by powers of Gauss curvature in Minkowski space.
Hongjie Ju
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The Gauss map in spaces of constant curvature [PDF]
Proceedings of the American Mathematical Society, 1973 Let N N be a complete simply connected Riemannian manifold of constant sectional curvature ≠ 0 \ne 0 . Let M M be an immersed Riemannian hypersurface of N N . The Gauss map on M M based at a point p p in N N is ...
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Curvature squared invariants in six-dimensional N $$ \mathcal{N} $$ = (1, 0) supergravity
Journal of High Energy Physics, 2019 We describe the supersymmetric completion of several curvature-squared invariants for N $$ \mathcal{N} $$ = (1, 0) supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and
Daniel Butter +4 more
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Prescription of Gauss curvature using optimal mass transport [PDF]
Geometriae Dedicata, 2016 In this paper we give a new proof of a theorem by Alexandrov on the Gauss curvature prescription of Euclidean convex sets. This proof is based on the duality theory of convex sets and on optimal mass transport. A noteworthy property of this proof is that it does not rely neither on the theory of convex polyhedra nor on P.D.E. methods (which appeared in
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Instability of elliptic equations on compact Riemannian manifolds with non-negative Ricci curvature
Electronic Journal of Differential Equations, 2010 We prove the nonexistence of nonconstant local minimizers for a class of functionals, which typically appear in scalar two-phase field models, over smooth N-dimensional Riemannian manifolds without boundary and non-negative Ricci curvature ...
Arnaldo S. Nascimento +1 more
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