Related papers: Remarks on "Spiral Minimal Products"
I suggest and examine artificial material which has exponentially degenerate vacuum state. The corresponding Hamiltonian contains only exotic four-spin interaction term. Each vacuum state is realized as a particular spin configuration…
We consider the collection of uniformly discrete point sets in Euclidean space equipped with the vague topology. For a point set in this collection, we characterise minimality of an associated dynamical system by almost repetitivity of the…
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that…
In this paper we introduce complex minimal Lagrangian surfaces in the bi-complex hyperbolic space and study their relation with representations in $\mathrm{SL}(3,\mathbb{C})$. Our theory generalizes at the same time minimal Lagrangian…
Consider a Stein manifold M obtained by plumbing cotangent bundles of manifolds of dimension greater than or equal to 3 at points. We prove that the Fukaya category of closed exact Lagrangians with vanishing Maslov class in M is generated…
A generalized Lagrangian for the description of hadronic matter based on the linear $SU(3)_L \times SU(3)_R$ $\sigma$-model is proposed. Besides the baryon octet, the spin-0 and spin-1 nonets, a gluon condensate associated with broken scale…
This article studies the deformation problem for compact special Lagrangians with boundary in a Calabi--Yau manifold, with each boundary component constrained along a given Lagrangian submanifold. The tangent vectors generating such…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
This is the fourth in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0303272 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n…
We introduce a joint project with Cheol-Hyun Cho on the construction of quantum-corrected moduli of Lagrangian immersions. The construction has important applications to mirror symmetry for pair-of-pants decompositions, SYZ and…
Since J. L. Lagrange initiated in 1760 the study of minimal surfaces of Euclidean 3-space, minimal surfaces in real space forms have been studied extensively by many mathematicians during the last two and half centuries. In contrast, so far…
We study geometry of the phase space for finite-dimensional dynamical systems with degenerate Lagrangians. The Lagrangian and Hamiltonian constraint formalisms are treated as different local-coordinate pictures of the same invariant…
We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions of canonical toric singularities (already found by…
Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratifed layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced…
We introduce and discuss notions of regularity and flexibility for Lagrangian manifolds with Legendrian boundary in Weinstein domains. There is a surprising abundance of flexible Lagrangians. In turn, this leads to new constructions of…
We study complex Lagrangians in Hitchin systems that factor through a proper subvariety of the Hitchin base non-trivially intersecting the regular locus. This gives a general framework for several examples in the literature. We compute the…
In this article we prove that for a large class of 2-dimensional minimal cones (including almost all 2-dimensional minimal cones that we know), the almost orthogonal union of any two of them is still a minimal cone. Comparing to existing…
We investigate the hyperfine splitting of the heavy baryons in the bound-state approach. We start with an ordinary relativistic Lagrangian which has been extensively used to discuss finite mass corrections to the heavy limit predictions. It…
We show that, for two-dimensional space-periodic incompressible flow, the solution can be evaluated numerically in Lagrangian coordinates with the same accuracy achieved in standard Eulerian spectral methods. This allows the determination…
In this work, merging ideas from compatible discretisations and polyhedral methods, we construct novel fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. The spaces and operators that appear in these…