- New Periodic Minimal Surfaces in H 3🔍
- New periodic minimal surfaces in H^3🔍
- Triply periodic minimal surface🔍
- New minimal surfaces in the hyperbolic space🔍
- the geometry and topology of singly|periodic minimal surfaces🔍
- Minimal Surfaces of Revolution in H3 and Their Global Stability🔍
- Schwarz H|Surfaces🔍
- The topological classification of minimal surfaces in R3🔍
New Periodic Minimal Surfaces in H 3
New Periodic Minimal Surfaces in H 3
We prove existence of new complete embedded minimal surfaces in H3 having the sym- metry of a regular tesselation by Coxeter orthoschemes. Each ...
New periodic minimal surfaces in H^3 - Project Euclid
Proceedings of the Centre for Mathematics and its Applications.
Triply periodic minimal surface - Wikipedia
TPMS have been observed as biological membranes, as block copolymers, equipotential surfaces in crystals etc. They have also been of interest in architecture, ...
New minimal surfaces in the hyperbolic space
We produce 2- and 3-parameter families of new minimal surfaces in H3, whose ... 7 Periodic minimal surfaces in H3. In this section, we describe the minimal ...
the geometry and topology of singly-periodic minimal surfaces
[7] MEEKS III, W. H. AND H. ROSENBERG, The global theory of doubly periodic minimal surfaces,. Invent. Math., 97 (1989), pp. 351-379.
Minimal Surfaces of Revolution in H3 and Their Global Stability - jstor
In Section 4, we show that some of the minimal surfaces of revolution in H3 obtained in Section 3 are globally stable. 2. Preliminaries. In the vector space R"+ ...
The Hexagonal or H-surface is one of the four triply periodic minimal surfaces discussed by Hermann Amandus Schwarz in his Preisschrift from 1867.
If we let A(R) denote the area of Em. Page 4. 684. CHARLES FROHMAN AND WILLIAM H. MEEKS III in the ball of radius R centered at the origin, then the results in ...
Continuous transitions of triply periodic minimal surfaces
Among various porous structures, triply periodic minimal surfaces (TPMS) have garnered extensive attention from researchers and engineers [1], [ ...
A Crystallographic Approach to 3-Periodic Minimal Surfaces
The 52 configurations of straight lines (2-fold rotation axes) that may be embedded within any 3-periodic intersection-free minimal surface are described in ...
chapter 3: minimal surfaces - The University of Chicago
The mean curvature H is the trace of the second fundamental form; i.e.. H(p) = X. IIp(ei,ei) where ei runs over an orthonormal basis for Tp.
Minimal surfaces in finite volume non compact hyperbolic 3-manifolds
In this paper we study the existence of periodic minimal surfaces in H3. More precisely, we consider surfaces in complete non compact hyperbolic.
A Construction Method for Triply Periodic Minimal Surfaces
A triply periodic minimal surface is a minimally immersed surface in Euclidean 3- space R3 which is invariant under translations in three independent directions ...
On 3-periodic minimal surfaces with non-cubic symmetry
On 3-periodic minimal surfaces with non-cubic symmetry · E. Koch, W. Fischer · Published 1988 · Mathematics · Zeitschrift für Kristallographie - Crystalline ...
Isoperimetric Properties of Some Genus 3 Triply Periodic Minimal ...
We can construct new minimal surfaces with the Weierstrass data (X, g, eiθdh) ... We know surfaces in H family have an order 3 rotation exist in the z direction ...
Periodic Minimal Surface - an overview | ScienceDirect Topics
Developments have made the parametrisation of more complicated periodic minimal surfaces possible (see Appendix), and the beautiful work of Karcher and ...
The Geometry of Periodic Minimal Surfaces. - EuDML
Rosenberg, H., and Meeks III, W.H.. "The Geometry of Periodic Minimal Surfaces.." Commentarii mathematici Helvetici 68.4 (1993): 538-578.
On bifurcation and local rigidity of triply periodic minimal surfaces in ...
3 for the local rigidity statement, and Theorem 5.4 for the bifurcation statement. We will recall in Section 6 the definitions of the H-family, the rPD-family,.
The gyroid and lidinoid functions are triply periodic minimal surfaces of genus 3 embedded in R3 ... H surfaces [1–3]. The gyroid function ...
NEW MINIMAL SURFACES IN S 3 - Project Euclid
Indeed, the fact that these surfaces contain great circles implies that they separate S3 into congruent components. Page 4. 172. H. KARCHER, U. PINKALL & I.