Related papers: The area minimizing problem in conformal cones
Consider a convex domain B of space. We prove that there exist complete minimal surfaces which are properly immersed in B. We also demonstrate that if D and D' are convex domains with D bounded and the closure of D contained in D' then any…
In this paper, we study a shape optimization problem for the torsional energy associated with a domain contained in an infinite cylinder, under a volume constraint. We prove that a minimizer exists for all fixed volumes and show some of its…
We study the metric of minimal area on a punctured Riemann surface under the condition that all nontrivial homotopy closed curves be longer than or equal to $2\pi$. By constructing deformations of admissible metrics we establish necessary…
In this paper, we propose a new assumption (1.2) that involves a small oscillation and $C^2$ norms for maps from smooth bounded domains into Euclidean spaces. Furthermore, by assuming that the domain has non-negative Ricci curvature, we…
The conformal field theory on a Z_N-surface is studied by mapping it on the branched sphere. Using a coulomb gas formalism we construct the minimal models of the theory.
This is a very brief report on recent developments on the Dirichlet problem for the minimal surface system and minimal cones in Euclidean spaces. We shall mainly focus on two directions: (1) Further systematic developments after…
This paper presents a canonical dual approach for solving nonconvex quadratic minimization problem. By using the canonical duality theory, nonconvex primal minimization problems over n-dimensional Lorentz cone can be transformed into…
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…
This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems…
We improve a lower bound for the smallest area of convex covers for closed unit curves from 0.0975 to 0.1, which makes it substantially closer to the current best upper bound 0.11023. We did this by considering the minimal area of convex…
Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. In…
This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the $s$-fractional perimeter and its minimizers, the $s$-minimal sets. We investigate the behavior…
We introduce a new family of closed differential forms naturally associated with minimal graphical submanifolds in Euclidean space, defined in arbitrary codimension. For each minimal graph, we construct an explicit closed form whose…
We consider vectorial problems in the calculus of variations with an additional pointwise constraint. Our admissible mappings ${\bf n}:\mathbb{R}^k\rightarrow \mathbb{R}^d$ satisfy ${\bf n}(x)\in M$, where $M$ is a manifold embedded in…
We study an area minimization problem for spacelike zero mean curvature surfaces in four dimensional Lorentz-Minkowski space. The areas of these surfaces are compared of with the areas of certain marginally trapped surfaces having the same…
We look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we…
We construct non-flat minimal capillary cones with bi-orthogonal symmetry groups for any dimension and contact angle. These cones interpolate between rescalings of a singular solution to the one-phase problem and the free-boundary cone…
We consider the numerical approximation of surfaces of prescribed Gaussian curvature via the solution of a fully nonlinear partial differential equation of Monge-Amp\`ere type. These surfaces need not be continuous up to the boundary of the…
The Plateau-Douglas problem asks to find an area minimizing surface of fixed or bounded genus spanning a given finite collection of Jordan curves in Euclidean space. In the present paper we solve this problem in the setting of proper metric…
It is a well-known fact that there exists a standard minimal embedding map for the Grassmannians of $n$-planes $G(n,m;\mathbb{F})(\mathbb{F}=\mathbb{R},\mathbb{C},\mathbb{H})$ and Cayley plane $\mathbb{O}P^2$ into Euclidean spheres, then an…