scholarly journals The Morse Index of a Minimal Surface

2021 ◽  
Vol 68 (06) ◽  
pp. 1
Author(s):  
Otis Chodosh ◽  
Davi Maximo
Keyword(s):  
Minimal Surface ◽  
Morse Index

scholarly journals The Existence of rG Family and tG Family, and Their Geometric Invariants

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1693
Author(s):  
Norio Ejiri ◽  
Toshihiro Shoda
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Morse Index ◽  
Space Groups ◽  
Geometric Invariants

In the 1990s, physicists constructed two one-parameter families of compact oriented embedded minimal surfaces in flat three-tori by using symmetries of space groups, called the rG family and tG family. The present work studies the existence of the two families via the period lattices. Moreover, we will consider two kinds of geometric invariants for the two families, namely, the Morse index and the signature of a minimal surface. We show that Schwarz P surface, D surface, Schoen’s gyroid, and the Lidinoid belong to a family of minimal surfaces with Morse index 1.

scholarly journals On the Morse index of branched Willmore spheres in 3-space

2021 ◽  
Vol 60 (4) ◽  
Author(s):  
Alexis Michelat
Keyword(s):  
Minimal Surface ◽  
Morse Index ◽  
Number Of Ends ◽  
General Method

AbstractWe develop a general method to compute the Morse index of branched Willmore spheres and show that the Morse index is equal to the index of certain matrix whose dimension is equal to the number of ends of the dual minimal surface (when the latter exists). As a corollary, we find that for all immersed Willmore spheres $$\vec {\Phi }:S^2\rightarrow \mathbb {R}^3$$ Φ → : S 2 → R 3 such that $$W(\vec {\Phi })=4\pi n$$ W ( Φ → ) = 4 π n , we have $$\mathrm {Ind}_{W}(\vec {\Phi })\le n-1$$ Ind W ( Φ → ) ≤ n - 1 .

Visualization of Enneper’s surface by line graphics

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 387-405 ◽  
Author(s):  
Vesna Velickovic
Keyword(s):  
Minimal Surface ◽  
Graphical Representations ◽  
Lines Of Curvature ◽  
Geodesic Lines

Here we study Enneper?s minimal surface and some of its properties. We compute and visualize the lines of self-intersection, lines of intersections with planes, lines of curvature, asymptotic and geodesic lines of Enneper?s surface. For the graphical representations of all the results we use our own software for line graphics.

Binding of Alkenes and Ionic Liquids to B–H-Functionalized Boron Nanoparticles: Creation of Particles with Controlled Dispersibility and Minimal Surface Oxidation

2015 ◽  
Vol 7 (18) ◽  
pp. 9991-10003 ◽  
Author(s):  
Jesus Paulo L. Perez ◽  
Jiang Yu ◽  
Anna J. Sheppard ◽  
Steven D. Chambreau ◽  
Ghanshyam L. Vaghjiani ◽  
...  
Keyword(s):  
Ionic Liquids ◽  
Minimal Surface ◽  
Surface Oxidation

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

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