Contracting convex hypersurfaces by curvature
WebExplore 134 research articles published on the topic of “Gaussian curvature” in 2016. Over the lifetime, 2726 publication(s) have been published within this topic receiving 50271 citation(s). Webto prove that convex hypersurfaces contract to points under speeds given by positive powers of the Gauss curvature, and adapted Huisken’s arguments to prove that the limiting shape is spherical under motion by the nth root of the Gauss curvature [C1] and later by the square root of the scalar curva-
Contracting convex hypersurfaces by curvature
Did you know?
WebFeb 1, 2024 · In this paper, we investigate closed strictly convex hypersurfaces in Rn+1 ℝ n + 1 which shrink self-similarly under a large family of fully nonlinear curvature flows by high powers of curvature.
WebJun 5, 2012 · We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain smooth and uniformly convex, and contract to points … WebNov 1, 2013 · In this paper, we study a class of fully nonlinear contracting curvature flows of closed, uniformly convex hypersurfaces in the Euclidean space $\mathbb R^{n+1}$ …
WebContracting convex hypersurfaces in Riemannian manifolds by their mean curvature Download PDF. Download PDF. Published: October 1986; Contracting convex … WebA new geometrical lemma is used to prove that any strictly convex compact initial hypersurface contracts to a point in finite time, becoming spherical in shape as the limit is approached. In the particular case of the mean curvature flow this provides a simple new proof of a theorem of Huisken. Download to read the full article text References
WebWe consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity. We prove that the ratio of circumradius to inradius is bounded by a function of the circumradius with limit 1 at zero.
WebOct 26, 2016 · This paper concerns the evolution of a closed convex hypersurface in ${\\mathbb{R}}^{n+1}$, in direction of its inner unit normal vector, where the speed is … mikrotik router price in bangladeshWebApr 5, 2011 · We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain... mikrotik router login password forgotWebJun 1, 2024 · A recent article Li and Lv (J. Geom. Anal. 30: 417–447, 2024) considered contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in... mikrotik run script from terminalWebAbstract. In this paper, we consider the contracting curvature flows of smooth closed surfaces in 3-dimensional hyperbolic space and in 3-dimensional sphere. In the hyperbolic case, we show that if the initial surface M_0 has positive scalar curvature, then along the flow by a positive power \alpha of the mean curvature H, the evolving surface ... mikrotik run script from netwatch hostWebIn this paper, we consider functionals related to mean curvature flow in an ambient space which evolves by an extended Ricci flow from the perspective introduced by Lott when studying a mean curvature flow in a Ricci flow background. One of them is a weighted extended version of the Gibbons-Hawking-York action on Riemannian metrics in … new world what to do with extra craft modsWebWe show that convex surfaces in an ambient three-sphere contract to round points in finite time under fully nonlinear, degree one homogeneous curvature flows, with no concavity condition on the speed. The result extends to convex axially symmetric hypersurfaces of the (n+1)-dimensional sphere. new world what to do with itemsWebApr 5, 2011 · Ben Andrews, James McCoy, Yu Zheng We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain smooth and uniformly convex, and contract to points after finite time. mikrotik script check interface status