Related papers: Comments on the regularity of harmonic maps betwee…

We study biharmonic maps between conformally compact manifolds, a large class of complete manifolds with bounded geometry, asymptotically negative curvature, and smooth compactification. These metrics provide a far-reaching generalization…

We establish the asymptotic regularity and the $\Delta$-convergence of the sequence constructed by the alternating projections to closed convex sets in a CAT($\kappa$) space with $\kappa > 0$. Furthermore, the strong convergence of the…

We consider critical points $u:\Omega\to N$ of the bi-energy \[ \int_\Omega |\Delta u|^2\,d x, \] where $\Omega\subset\mathbb{R}^m$ is a bounded smooth domain of dimension $m\ge 5$ and $N\subset\mathbb{R}^L$ a compact submanifold without…

We study harmonic map sequences from surfaces to compact homogeneous spaces. For sequences developing a single bubble, we derive refined asymptotic expansions in the neck region and prove new obstruction relations among the leading…

We prove partial and full boundary regularity for manifold constrained $p(x)$-harmonic maps.

We prove a couple of results on local continuous extension of proper holomorphic maps $F:D \rightarrow \Omega$, $D, \Omega \varsubsetneq \mathbb{C}^n$, making local assumptions on $\partial{D}$ and $\partial{\Omega}$. The first result…

We review some regularity results for the Laplacian and $p$-Laplacian in metric measure spaces. The focus is mainly on interior H\"older, Lipschitz and second-regularity estimates and on spaces supporting a Poincar\'e inequality or having…

This article introduces innovative classes of open sets in \(\mathbb{R}^{N}\), where \(N=2, 3\), characterized by a geometric property associated with the inward normal. The focus lies on proving compactness results for the Hausdorff…

Let N and P be smooth manifolds of dimensions n and p (n \geq p \geq 2) respectively. Let \Omega(N,P) denote an open subspace of J^{infty}(N,P) which consists of all regular jets and jets with prescribed singularities of types A_{i}, D_{j}…

We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight H\"older-behavior for this operation under minimal assumptions. Our…

We consider triholomorphic maps from an almost hyper-Hermitian manifold $\mathcal{M}^{4m}$ into a hyperK\"ahler manifold $\mathcal{N}^{4n}$. This means that $u \in W^{1,2}$ satisfies a quaternionic del-bar equation. We work under the…

We consider a bounded Lipschitz domain $\Omega\subseteq\mathbb{R}^3$ with sufficiently smooth boundary and prove piecewise Sobolev regularity of vector fields that have piecewise regular curl and divergence, but may be discontinuous across…

Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain…

Given $\Omega\subset \mathbb{R}^n$ with $n\geq 2$, $D\subset \Omega$ open, and $u:\Omega \to \mathbb{R}^m$, we study elliptic systems of the type $$ {\rm div} \big( ( A + (B- A)\chi_D)\nabla u\big) = 0 \quad \text{in $\Omega\cap B_1$,} $$…

We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove…

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…

We study the limiting behavior of minimizing $p$-harmonic maps from a bounded Lipschitz domain $\Omega \subset \mathbb{R}^{3}$ to a compact connected Riemannian manifold without boundary and with finite fundamental group as $p \nearrow 2$.…

We study the regularity of Radon measures $\mu$ which satisfy that there exists a function $h_\mu$ in $H^1(\Omega)$, stationary harmonic such that $\Delta h_\mu =\mu$ in $\Omega$ (here $\Omega$ is an open set of $\mathbb{R}^2$). Such…

We consider H\"older continuous weak solutions $u\in C^\gamma(\Omega)$, $u\cdot n|_{\partial \Omega}=0$, of the incompressible Euler equations on a bounded and simply connected domain $\Omega\subset\mathbb{R}^d$. If $\Omega$ is of class…

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.