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The normalized curve shortening flow and homothetic solutions
The curve shortening problem, by now widely known, is to understand the evolution of regular closed curves γ: R/Z -> M moving according to the curvature normal vector: dy/dt = kN = -"the ZΛgradient
A Hopf differential for constant mean curvature surfaces inS2×R andH2×R
A basic tool in the theory of constant mean curvature (cmc) surfaces Σ in space forms is the holomorphic quadratic differential discovered by H. Hopf. In this paper we generalize this differential to
On complete manifolds with nonnegative Ricci curvature
Complete open Riemannian manifolds (Mn, g) with nonnegative sectional curvature are well understood. The basic results are Toponogov's Splitting Theorem and the Soul Theorem [CG1]. The Splitting
Constant mean curvature tori in terms of elliptic functions.
Based on a numerical approximation of such a solution, we could produce plots of one ff-torus. In these Computer generated pictures the curvature lines for the smaller principal curvature λ^ looked
Isoparametric hypersurfaces with four or six distinct principal curvatures
This invention relates to substrates and articles of manufacture incorporating a fluoropolymer primer coating. The primer coating comprises a copolymer of ethylene and a halogenated comonomer
Lower curvature bounds, Toponogov's theorem, and bounded topology. II
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1985, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.
Injectivity Radius Estimates and Sphere Theorems
We survey results about the injectivity radius and sphere theorems, from the early versions of the topological sphere theorem to the authors’ most recent pinching below1 4 theorems, explaining at
A basic tool in the theory of constant mean curvature (cmc) surfaces 2 in space forms is the holomorphic quadratic dierential dis- covered by H. Hopf. In this paper we generalize this dierential to
Wiedersehen metrics and exotic involutions of Euclidean spheres
Abstract We provide explicit, simple, geometric formulas for free involutions ρ of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient Sn/ρ is a manifold that