minimal surfaces
Bubbling analysis and geometric convergence results for free boundary minimal surfaces
... Here is the first application we wish to discuss: since we can fully classify bubbles and half-bubbles of Morse index less than two (see Corollary 22 and Corollary 24) we can then get novel, unconditional, geometric ...
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A Note on Polynomial type Minimal Surfaces
... ABSTRACT: In this paper, we develop two new minimal surfaces of degree six in parametric polynomial form with isothermal parameter. Graphical representations in different angles have been presented. All ...
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A gap theorem for free boundary minimal surfaces in the three ball
... on surfaces of this topological type that maximize the first Steklov eigenvalue with fixed boundary ...boundary minimal surfaces in B 3 of genus zero or one, and with any number ...
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Minimal Surfaces and Gauss Curvature of Conoid in Fins ler Spaces with (α, β) Metrics
... of minimal surfaces in Euclidean space has developed into a rich branch of differential ...of minimal surfaces have been found in Euclidean ...study minimal surfaces with ...
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Equivariant minimal surfaces in CH2 and their Higgs bundles
... thereby to Higgs bundles [10, 29, 9, 43], Our starting point is two facts: (i) to each irreducible ρ and marked conformal structure on Σ (i.e., conjugacy class of Fuchsian representations) there is a ρ-equivariant ...
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Holomorphic curves and minimal surfaces in Kähler manifolds
... The following results of Micallef [37] and Micallef-Wolfson [38] give a fairly complete description of the relation between holomorphicity and stability of minimal surfaces in hyperldihl[r] ...
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Periodic minimal surfaces of cubic symmetry
... periodic surfaces with congruent labyrinths are called balance ...balance surfaces and found a large number of new triply periodic minimal balance surfaces ...known surfaces could arise ...
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Numerical modelling of stable minimal surfaces
... The numerical modelling of minimal surfaces is presented, based initially on the discretisation of the form using plane linear line and triangular elements.. The application of the matri[r] ...
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Visualizing Minimal Surfaces »
... In what follows, we first provide some background from minimal surface theory. This includes a review of classical surface theory, a description of the Weierstrass represen- tation, a summary of pertinent facts ...
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Foliations by minimal surfaces and contact structures on certain closed 3 manifolds
... Condition (a) guarantees that, for basic vector fields {X, Y } above, ᐂ [X, Y ] is globally defined on M and, simultaneously in the foliation case, that the leaves of H are minimal surfaces of M. If the flow F ...
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Topological properties of minimal surfaces
... about minimal surfaces in R ...for minimal surfaces, discussed in the Introduction: i f P and G are stable minimal surfaces and f is an arc joining SF to iG, then the bridge ...
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Flowing maps to minimal surfaces
... We introduce a flow of maps from a compact surface of arbitrary genus to an arbitrary Riemannian manifold which has elements in common with both the harmonic map flow and the mean curvature flow, but is more effective at ...
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Physics and mathematics of interfaces in self-assemblies : studies in electrostatics and triply periodic minimal surfaces
... Having dispensed with the regular class restriction that only branch points of the same order are superposed on the Riemann surface, the underlying basis is now extended to all fifteen S[r] ...
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Nonparametric minimal surfaces in R3 whose boundaries have a jump discontinuity
... How does the generalized solution of the Dirichlet problem for the minimal surface equation with boundary values.. say at the origin.[r] ...
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Minimal surfaces
... In this section the following definition consists of the properties that a surface in space R3 must satisfy, where surfaces have no sharp point, edges, or self-intersection. Definition 1.1.1. A surface in R3 is a ...
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On the existence of minimal surfaces with free boundary
... If we assume the Douglas Condition in 7.34 for the homotopy classes o f maps defined by 1.1, 1.2 and 1.3, then there exists a minimal surface with genus g in each of these homotopy class[r] ...
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Differential geometry of surfaces and minimal surfaces
... X^, along our"curve"(a line) lying in the surface as depicted in figure 22.. Here, ail these vectors along the line lare the same vector being translated along Iand are all ta[r] ...
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Simulation of Acoustic Wave Propagation in 3-D Sonic Crystals based on Triply Periodic Minimal Surfaces
... Discovered by Schoen in 1970 [5], the gyroid is an infinitely connected triply periodic minimal surface containing no straight lines. Essentially, it consists of a single surface folded in such a way that the mean ...
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Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS(5) x S-5
... representing 1/4 BPS Wilson loop in planar N =4 SYM theory pre- viously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of ...
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On area comparison and rigidity involving the scalar curvature
... stable minimal surfaces and the scalar curvature S of the ambient 3-manifold M ...stable, minimal surface in a 3-manifold of positive scalar curvature must have genus ...
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