Related papers: Bubble tree convergence for harmonic maps into com…

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,…

In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…

We generalize the notion of calibrated submanifolds to smooth maps and show that the several examples of smooth maps appearing in the differential geometry become the examples of our situation. Moreover, we apply these notion to give the…

A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric…

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…

Let $S$ be a punctured Riemann surface with Euler characteristic $\chi(S)<0$. For any unitary representation $\rho: \pi_1(S) \to U(N)$, we introduce its renormalized energy and its harmonic representatives, which are equivariant harmonic…

We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…

Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…

We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families…

We announce a generalization of Zimmer's cocycle superrigidity theorem proven using harmonic map techniques. This allows us to generalize many results concerning higher rank lattices to all lattices in semisimple groups with property $(T)$.…

We consider minimising $p$-harmonic maps from three-dimensional domains to the real projective plane, for $1<p<2$. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular…

We use the language of proper CAT(-1) spaces to study thick, locally compact trees, the real, complex and quaternionic hyperbolic spaces and the hyperbolic plane over the octonions. These are rank 1 Euclidean buildings, respectively rank 1…

In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…

We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the…

We establish the boundary regularity of harmonic maps from $RCD(K, N)$ metric measure spaces into $CAT(0)$ metric spaces.

We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathcal{H}^N)$. Under the sole (necessary) assumption that the measure of unit balls is…

For conformal metrics with conical singularities and positive curvature on $\mathbb S^2$, we prove a convergence theorem and apply it to obtain a criterion for nonexistence in an open region of the prescribing data. The core of our study is…

We prove compactness with respect to $\Gamma$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free…

Energy minimizing harmonic maps between manifolds are known to be smooth outside a rectifiable set of codimension $3$, called the singular set. The possibility that this set is not a manifold, but has arbitrarily many small gaps in it, is…

We study a version of Calder\'on's problem for harmonic maps between Riemannian manifolds. By using the higher linearization method, we first show that the Dirichlet-to-Neumann map determines the metric on the domain up to a natural gauge…