Results 11 to 20 of about 998,625 (264)
Curvature and solidification [PDF]
Journal of Computational Physics, 1985 A method is presented for finding the osculating circle, and thus the curvature and the normal, of a curve defined by an array of partial volumes. This method is applied, within the framework of an enthalpy formulation, to the solutions of model equations that describe the motion of a front separating ice and supercooled water.
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A rigidity theorem for nonvacuum initial data [PDF]
, 2001 In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature.
Choquet-Bruhat Y. +10 more
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Mean Curvature in the Light of Scalar Curvature [PDF]
Annales de l'Institut Fourier, 2020 We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
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Geometric Mean Curvature Lines on Surfaces Immersed in R3 [PDF]
, 2002 Here are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature $\mathcal K$ is positive) of an oriented surface immersed in $\mathbb R^3$.
Garcia, Ronaldo, Sotomayor, Jorge
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On the semicontinuity of curvatures [PDF]
Commentarii Mathematici Helvetici, 1992 For a convex body \(K\) in \(\mathbb{R}^ n\) with a boundary of class \(C^ 2\) and positive curvatures and for \(\alpha\in\mathbb{R}\backslash\{0\}\) and \(j=1,\ldots,n-1\), let \[ \psi^ \alpha_ j(K)=\left\{{1\over\omega_ n}\int_{S^{n-1}}s_ j(K,u)^ \alpha d\omega(u)\right\}^{1/\alpha}, \] where \(s_ j(K,u)\) is the normalized \(j\)-th elementary ...
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A general convergence result for the Ricci flow in higher dimensions [PDF]
, 2008 Let (M,g_0) be a compact Riemannian manifold of dimension n \geq 4. We show that the normalized Ricci flow deforms g_0 to a constant curvature metric provided that (M,g_0) x R has positive isotropic curvature.
Brendle, S.
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Nonpositivity: Curvature vs. curvature operator [PDF]
Proceedings of the American Mathematical Society, 2004 It is shown that there exist closed Riemannian manifolds M M all of whose sectional curvatures are negative, but M M does not admit any metric with nonpositive curvature operator.
F. T. Farrell, C. S. Aravinda
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Mathematische Annalen, 2015 The purpose of this paper is to interpret the phase transition in the Loewner theory as an analog of the hyperbolic variant of the Schur theorem about curves of bounded curvature. We define a family of curves that have a certain conformal self-similarity property. They are characterized by a deterministic version of the domain Markov property, and have
Lind, Joan, Rohde, Steffen
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Affine curvature homogeneous 3-dimensional Lorentz Manifolds
, 2005 We study a family of 3-dimensional Lorentz manifolds. Some members of the family are 0-curvature homogeneous, 1-affine curvature homogeneous, but not 1-curvature homogeneous. Some are 1-curvature homogeneous but not 2-curvature homogeneous.
Gilkey, P., Nikcevic, S.
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On the total curvatures of a tame function
, 2008 Given a definable function f, enough differentiable, we study the continuity of the total curvature function t --> K(t), total curvature of the level {f=t}, and the total absolute curvature function t-->|K| (t), total absolute curvature of the level {f=t}
A. Bernig +11 more
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