Related papers: Singular Behavior of Harmonic Maps Near Corners

We prove partial regularity of weakly stationary harmonic maps with (partially) free boundary data on manifolds where the domain metric may degenerate or become singular along the free boundary at the rate $d^\alpha$ for the distance…

In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):…

In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions…

We study the map from conductances to edge energies for harmonic functions on finite graphs with Dirichlet boundary conditions. We prove that for any compatible acyclic orientation and choice of energies there is a unique choice of…

The singular set of a generic map $f: M\to F$ of a manifold $M$ of dimension $m\ge 2$ to an oriented surface $F$ is a closed smooth curve $\Sigma(f)$. We study the parity of the number of components of $\Sigma(f)$. The image $f(\Sigma)$ of…

Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…

The convolution properties are discussed for the complex-valued harmonic functions in the unit disk $\mathbb{D}$ constructed from the harmonic shearing of the analytic function $\phi(z):=\int_0^z…

Many authors have examined various boundary behaviors of injective harmonic mappings in the open unit disk. Building on Laugesen's work, Bshouty and others explored the boundary behavior of harmonic mappings under different conditions. In…

Let $\ast$ and $\widetilde {\ast}$ denote the convolution of two analytic maps and that of an analytic map and a harmonic map respectively. Pokhrel [1] proved that if $f = h+\overline{g}$ is a harmonic map convex in the direction of…

The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its…

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…

A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…

We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called {\em pseudoharmonic morphisms}, include harmonic morphisms…

Let $(M, g)$, $(N, h)$ be compact Riemannian manifolds without boundary, and let $f$ be a smooth map from $M$ into $N$. We consider a covariant symmetric tensor $T_f$ $=$ ${\displaystyle f^*h - \frac{1}{m} |df|^2 g}$, where $f^*h$ denotes…

We study spaces with a cuspidal (or horn-like) singularity embedded in a smooth Riemannian manifold and analyze the geodesics in these spaces which start at the singularity. This provides a basis for understanding the intrinsic geometry of…

We study certain topological problems that are inspired by applications to autonomous robot manipulation. Consider a continuous map $f\colon X\to Y$, where $f$ can be a kinematic map from the configuration space $X$ to the working space $Y$…

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…

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…

We study the degrees of homogeneous harmonic maps between simplicial cones. Such maps have been used to model the local behavior of harmonic maps between singular spaces, where the degrees of homogeneous approximations describe the…

The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of…