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Gaussian Curvature and the Gauss Map
2001We shall now introduce two new measures of the curvature of a surface, called its gaussian and mean curvatures. Although these together contain the same information as the two principal curvatures, they turn out to have greater geometrical significance.
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Gauss Inner Curvature of Surfaces
1997Gauss discovers a number of properties of two-dimensional submanifolds of ℝ3, which can be understood as M 2, that is, as two-dimensional differential manifolds ‘on their own’ i.e., without any reference to the question if they are isomorphically imbedded in ℝ3 or not.
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Rotationally symmetric translators of the Gauss curvature flow
2023Summary: We completely classify in Euclidean 3-space the rotational translators of the flow by powers of the Gauss curvature. This classification is also extended to Lorentz-Minkowski 3-space.
Aydin, Muhittin Evren +1 more
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Deforming a hypersurface by its Gauss‐Kronecker curvature
Communications on Pure and Applied Mathematics, 1985The following theorem is proved: Let X(s), \(s\in S^ n\) (the unit sphere), be a smooth, closed, strictly convex hypersurface in \({\mathbb{R}}^{n+1}\). Then the initial value problem \[ \frac{\partial X}{\partial t}(s,t)=-k(s,t)N(s,t),\quad X(s,0)=X(s), \] where k is the Gauss-Kronecker curvature and N is the outer unit normal at X(x,t), has a unique,
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Pattern selection on axial-compressed bilayer systems with a non-zero Gauss curvature
Journal of the Mechanics and Physics of Solids, 2021Yanping Cao
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Convergence of Gauss curvature flows to translating solitons
Advances in Mathematics, 2022Kyeongsu Choi, Panagiota Daskalopoulos
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