Related papers: Simplicial energy and simplicial harmonic maps

Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…

Given a topological cell decomposition of a closed surface equipped with edge weights, we consider the Dirichlet energy of any geodesic realization of the 1-skeleton graph to a hyperbolic surface. By minimizing the energy over all possible…

We introduce and analyze numerical companion matrix methods for the reconstruction of hypersurfaces with crossings from smooth interpolants given unordered or, without loss of generality, value-sorted data. The problem is motivated by the…

In this paper, we introduce the stress-energy tensors of the partial energies E'(f) and E"(f) of maps between Kaehler manifolds. Assuming the domain manifolds poss some special exhaustion functions, we use these stress-energy tensors to…

We apply our abstract gradient inequalities developed by the authors in arXiv:1510.03817 to prove Lojasiewicz--Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity…

We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy…

Minimal surfaces in $\mathbb{R}^n$ can be locally approximated by graphs of harmonic functions, i.e., functions that are critical points of the Dirichlet energy, but no analogous theorem is known for $H$-minimal surfaces in the…

In the case where both the domain and target manifolds are almost Hermitian, we introduce the concept of Hermitian pluriharmonic maps. We prove that any holomorphic or anti-holomorphic map between almost Hermitian manifolds is Hermitian…

We derive the energy of the surface between the normal and superfluid components of a mixed phase of a system composed of two particle species with different densities. The surface energy is obtained by the integration of the free energy…

We study Dirac-harmonic maps from surfaces to manifolds with torsion, which is motivated from the superstring action considered in theoretical physics. We discuss analytic and geometric properties of such maps and outline an existence…

In this paper we present a procedure to integrate, up to quadratures, the matching conditions of the energy shaping method. We do that in the context of underactuated Hamiltonian systems defined by simple Hamiltonian functions. For such…

Motivated by the theory of harmonic maps on Riemannian surfaces, conformal-harmonic maps between two Riemannian manifolds $M$ and $N$ were introduced in search of a natural notion of harmonicity for maps defined on a general even…

In this paper, we study the Lusternik-Schnirelmann category of a simplicial map between simplicial complexes, generalizing the simplicial category of a complex to that of a map. Several properties of this new invariant are shown, including…

Geometric and topological bounds are obtained for the first energy level gap of a particle constrained to move on a compact surface in 3-space. Moreover, geometric properties are found which allows for stationary and uniformly distributed…

We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds…

In the standard treatment of heterogeneous nucleation on a surface, the energy of the surface is assumed to be homogeneous. Often its value is obtained from some macroscopic measurement. We ask the question what happens if we consider the…

This paper defines the basis of a new hierarchical framework for segmentation algorithms based on energy minimization schemes. This new framework is based on two formal tools. First, a combinatorial pyramid encode efficiently a hierarchy of…

An ODE variational calculation shows that an image principle curvature ratio factor can raise the lower bound, 2(Image Area), on energy of a harmonic map of a surface into Rn. In certain situations, including all radially symmetry harmonic…

In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of…