Related papers: Alday-Maldacena duality and AdS Plateau problem
We discuss some geometrical issues related to spacelike minimal surfaces in $AdS_m$ with null polygonal boundaries at conformal infinity. In particular for $AdS_4$, two holomorphic input functions for the Pohlmeyer reduced system are…
We solve explicitly the crossing equation under sufficiently general assumptions on the structure of the dressing phase. We obtain the BES/BHL dressing phase as a minimal solution of the crossing equation and identify the possible CDD…
It is known that self-duality equations for multi-instantons on a line in four dimensions are equivalent to minimal surface equations in three dimensional Minkowski space. We extend this equivalence beyond the equations of motion and show…
In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if $\Sigma$ is a $2$-dimensional embedded minimal surface, then the knowledge of the…
Plateau's problem is not a single conjecture or theorem, but rather an abstract framework, encompassing a number of different problems in several related areas of mathematics. In its most general form, Plateau's problem is to find an…
We study certain obstacle type problems involving standard and nonlocal minimal surfaces. We obtain optimal regularity of the solution and a characterization of the free boundary.
The difficulty in exploring potential energy surfaces, which are nonconvex, stems from the presence of many local minima, typically separated by high barriers and often disconnected in configurational space. We obtain the global minimum on…
We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that…
We introduce a description of a minimal surface in a space with boundary, as the world-hypersurface that the entangling surface traces. It does so by evolving from the boundary to the interior of the bulk under an appropriate geometric…
We present the novel method for generation of periodic surfaces based on the simple Landau-Ginzburg model of microemulsion. We test the method on four minimal surfaces (P,D,G, and I-WP), find two new surfaces of cubic symmetry, show how to…
We prove some non-existence results for the asymptotic Plateau problem of minimal and area minimizing surfaces in the homogeneous space ${\widetilde{\mathrm{SL}}_2(\mathbb{R})}$ with isometry group of dimension 4, in terms of their…
An extended version of the AdS/QCD Soft-Wall model that incorporates QCD-like anomalous contributions to the dimensions of gauge theory operators is proposed. This exploratory approach leads to a relation between scalar glueball masses and…
Minimal surfaces are among the most natural objects in Differential Geometry, and have been studied for the past 250 years ever since the pioneering work of Lagrange. The subject is characterized by a profound beauty, but perhaps even more…
We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the…
We consider the Pohlmeyer reduction for spacelike minimal area worldsheets in AdS$_5$. The Lax pair for the reduced theory is found, and written entirely in terms of the $A_3=D_3$ root system, generalizing the $B_2$ affine Toda system which…
We investigate AdS/QCD duality for the two-point correlation function of the lowest dimension scalar glueball operator, in the case of the IR soft wall model. We point out the role of the boundary conditions for the bulk-to-boundary…
It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…
In this paper, our goal is solving backward doubly stochastic differential equation (BDSDE for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic…
We investigate minimal surfaces in products of two-spheres ${\mathbb S}^2_p\times {\mathbb S}^2_p$, with the neutral metric given by $(g,-g)$. Here ${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$ , and $g$ is the induced metric on the sphere.…
Toda lattice and minimal surfaces are related to each other through Allen-Cahn equation. In view of the structure of the solutions of the Toda lattice, we find new balancing configuration using techniques of integrable systems. This allows…