Journal Article10.1007/BF01389060
Hopf tori inS 3
225
About: This article is published in Inventiones Mathematicae. The article was published on 01 Jun 1985.
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Configurations of fluid membranes and vesicles
TL;DR: In this article, the authors describe the systematic physical theory developed to understand the static and dynamic aspects of membrane and vesicle configurations, and the preferred shapes arise from a competition between curvature energy which derives from the bending elasticity of the membrane, geometrical constraints such as fixed surface area and fixed enclosed volume, and a signature of the bilayer aspect.
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Min-Max theory and the Willmore conjecture
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TL;DR: In this paper, it was shown that the integral of the square of the mean curvature of a torus immersed in R 3 is at least 2 2, using the min-max theory of minimal surfaces.
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Min-Max theory and the Willmore conjecture
Fernando C. Marques,André Neves +1 more
TL;DR: In this paper, the integral of the square of the mean curvature of a torus immersed in Euclidean three-space is shown to be at least 2 π 2 φ 2, using the min-max theory of minimal surfaces.
254
General helices and a theorem of Lancret
Manuel Barros
- 01 Jan 1997
TL;DR: In this article, a theorem of Lancret for general helices in a 3-dimensional real-space-form is presented, which gives a relevant difference between hyperbolic and spherical geometries.
Lectures on Elastic Curves and Rods
David A. Singer
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TL;DR: In this article, a tutorial on the Euler elastica and the Kirchhoff elastic rod is presented. And the authors consider the classical variational problem in Euclidean space and its generalization to Riemannian manifolds.
References
•Book
Lecture Notes on Elementary Topology and Geometry.
Isadore Manuel Singer,J. A. Thorpe +1 more
- 01 Jan 1967
TL;DR: In this paper, the Tychonoff theorem was used to prove separation axioms and separation by continuous functions in the point set topology of Riemannian geometry of surfaces.