Related papers: Simplicial energy and simplicial harmonic maps

Deciding realizability of a given polyhedral map on a (compact, connected) surface belongs to the hard problems in discrete geometry, from the theoretical, the algorithmic, and the practical point of view. In this paper, we present a…

For any twisted ideal polygon in $\mathbb{H}^3$, we construct a harmonic map from $\mathbb{C}$ to $\mathbb{H}^3$ with a polynomial Hopf differential, that is asymptotic to the given polygon, and is a bounded distance from a pleated plane.…

For a fixed smooth map $u_0$ between two Riemann surfaces $\Sigma$ and $S$ with non-zero degree, we consider the energy function on Teichm\"uller space $\mc{T}$ of $\Sigma$ that assigns to a complex structure $t\in \mc{T}$ on $\Sigma$ the…

We prove the energy identity for min-max sequences of the Sacks-Uhlenbeck and the biharmonic approximation of harmonic maps from surfaces into general target manifolds. The proof relies on Hopf-differential type estimates for the two…

We consider conformal immersions of Riemann surfaces in $\bb{S}^4$ and study their Gauss maps with values in the Grassmann bundle $\mathcal{F} = SO_5/T^2 \to \mathbb{S}^4$. The energy of maps from Riemann surfaces into $\mathcal{F}$ is…

The Image-Computing Spectral Sequence computes the homology of the image of a finite map from the alternating homology of the multiple point spaces of the map. A related spectral sequence was obtained by Gabrielov, Vorobjob and Zell which…

We prove lower bounds for energy functionals of mappings from real, complex and quaternionic projective spaces to Riemannian manifolds. For real and complex projective spaces, these lower bounds are sharp, and we characterize the family of…

I use harmonic maps and minimal surfaces to study quadratic equations in groups.

We study the existence and regularity of energy-minimizing harmonic almost complex structures. We have proved results similar to the theory of harmonic maps, notably the classical results of Schoen-Uhlenbeck and recent advance by…

We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of…

In this note we demonstrate how the analogy between the harmonic Gauss map of a constant mean curvature surface and the harmonic conformal Gauss map of a Willmore surface can be used to obtain results on Willmore surfaces.

We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…

In this work, we define the Laplacian and Normalized Laplacian energies of vertices in a graph, we derive some of its properties and relate them to combinatorial, spectral and geometric quantities of the graph.

In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…

We prove uniqueness of equivariant harmonic maps into irreducible symmetric spaces of non-compact type and Euclidean buildings associated to isometric actions by Zariski dense subgroups.

We study a second order differential equation corresponding to rotationally symmetric $F$-harmonic maps between certain noncompact manifolds. We show unique continuation and Liouville's type theorems for positive solutions. Asymptotic…

Concavity properties prevent the existence of significant landscapes in energy surfaces obtained by strict constrained energy minimizations. The inherent contradiction is due to fluctuations of collective coordinates. A solution to those…

A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…

Let $\varphi\in C^0 \cap W^{1,2}(\Sigma, X)$ where $\Sigma$ is a compact Riemann surface, $X$ is a compact locally CAT(1) space, and $W^{1,2}(\Sigma,X)$ is defined as in Korevaar-Schoen. We use the technique of harmonic replacement to prove…

We derive a lower bound for energies of harmonic maps of convex polyhedra in $ \R^3 $ to the unit sphere $S^2,$ with tangent boundary conditions on the faces. We also establish that $C^\infty$ maps, satisfying tangent boundary conditions,…