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The Variational Origin of Motion by Gaussian Curvature
, 2007 A variational formulation of an image analysis problem has the nice feature that it is often easier to predict the effect of minimizing a certain energy functional than to interpret the corresponding Euler-Lagrange equations. For example, the equations of motion for an active contour usually contains a mean curvature term, which we know will ...
Niels Chr. Overgaard, Jan Erik Solem
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The Gaussian and mean curvature criteria for curvature continuity between surfaces
Computer Aided Geometric Design, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiuzi Ye
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Variation of gaussian curvature under conformal mapping and its application
Computers and Mathematics With Applications, 1993 We characterize conformal mapping between two surfaces, S and S∗, based on Gaussian curvature before and after motion. An explicit representation of the Gaussian curvature after conformal mapping is presented in terms of Riemann-Christoffel tensor and ...
D B Goldgof, C Kambhamettu
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Journal of Differential Equations, 2021
The authors study the Nirenberg problem on \(S^2\): Given a smooth function \(f:S^2\to\mathbb{R}\) which is positive somewhere, does there exist a metric \(g\) on \(S^2\) conformally equivalent to the standard metric \(g_0\) and having Gaussian curvature \(f\). The main theorem states that a solution exists under the following assumptions. (a) Critical
Xuezhang Chen +3 more
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The authors study the Nirenberg problem on \(S^2\): Given a smooth function \(f:S^2\to\mathbb{R}\) which is positive somewhere, does there exist a metric \(g\) on \(S^2\) conformally equivalent to the standard metric \(g_0\) and having Gaussian curvature \(f\). The main theorem states that a solution exists under the following assumptions. (a) Critical
Xuezhang Chen +3 more
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Gaussian Curvature, Mirrors, and Maps
The American Mathematical Monthly, 2012We present a method to optically measure the Gaussian curvature K of a surface and show how it can be used to establish a link between surfaces with constant K and area preserving maps between a sp...
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Graph Regularisation Using Gaussian Curvature
2009This paper describes a new approach for regularising triangulated graphs. We commence by embedding the graph onto a manifold using the heat-kernel embedding. Under the embedding, each first-order cycle of the graph becomes a triangle. Our aim is to use curvature information associated with the edges of the graph to effect regularisation.
Hewayda ElGhawalby, Edwin R. Hancock
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Gaussian-curvature-derived invariants for isometry
Science China Information Sciences, 2012Surface deformations without tearing or stretching, preserving the intrinsic properties, are called isometries. This paper presents a new definition of Gaussian curvature moments (GCMs) by the integral of n power of Gaussian curvature. Then a series of moment invariants, called Gaussian curvature moment invariants (GCMIs), are derived via GCMs.
Weiguo Cao +4 more
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Gaussian and mean curvatures of rational maps
Computer Aided Geometric Design, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Gaussian and Geodesic Curvature of Riemannian Manifolds
Canadian Journal of Mathematics, 1974In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:Here, c is a suitable constant depending on the dimension of M and Ω is an n-form (n = dim M) which may be calculated from its curvature tensor. W.
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On the Gaussian curvature of the indicatrix of a Lagrange space
1991Let \(R^n\) be an \(n\)-dimensional Euclidean space and \((R^n,L)\) a Lagrange space with \(L\) a smooth function in the tangent bundle of \(R^n\) satisfying a certain regularity condition. For \(L=F^2\) with \(F\) homogeneous of degree one we have a Finsler space.
NISHIMURA, Shin-ichi, HASHIGUCHI, Masao
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