Related papers: Generalized neck analysis of harmonic maps from su…

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…

The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…

In this paper, we prove some refined estimate in the neck region when a sequence of harmonic maps from surfaces blow up. The new estimate allows us to see the shape of the center of the neck region. As an application, we prove an inequality…

In this paper, we formulate and prove a general compactness theorem for harmonic maps using Deligne-Mumford moduli space and families of curves. The main theorem shows that given a sequence of harmonic maps over a sequence of complex…

In this paper we study upper and lower bounds of the index and the nullity for sequences of harmonic maps with uniformly bounded Dirichlet energy from a two-dimensional Riemann surface into a compact target manifold. The main difficulty…

We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We…

We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in $W^{1,2}$ and…

We study geometrically constrained magnetic walls in a three dimensional geometry where two bulks are connected by a thin neck. Without imposing any symmetry assumption on the domain, we investigate the scaling of the energy as the size of…

So far magnetic domain walls in one-dimensional structures have been described theoretically only in the cases of flat strips, or cylindrical structures with a compact cross-section, either square or disk. Here we describe an extended phase…

We prove the energy identity and the no neck property for a sequence of smooth extrinsic polyharmonic maps with bounded total energy.

Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…

In this paper we find analogues for $\varepsilon$-harmonic maps to the generalised energy identity and the existence of geodesic necks result discovered by Yuxiang Li and Youde Wang for $\alpha$-harmonic maps. In particular there exist…

The ground state of interacting particles on a disordered one-dimensional host-lattice is studied by a direct numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice…

We explore geometric aspects of bubble convergence for harmonic maps. More precisely, we show that the formation of bubbles is characterised by the local excess of curvature on the target manifold. We give a universal estimate for curvature…

Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…

In this article, we prove energy quantization for approximate (intrinsic and extrinsic) biharmonic maps into spheres where the approximate map is in $L \log L$. Moreover, we demonstrate that if the $L\log L$ norm of the approximate maps…

We study the statistical properties of interstellar dust polarization at high Galactic latitude, using the Stokes parameter Planck maps at 353 GHz. Our aim is to advance the understanding of the magnetized interstellar medium (ISM), and to…

Learning the structure--dynamics correlation in disordered systems is a long-standing problem. Here, we use unsupervised machine learning employing graph neural networks (GNN) to investigate the local structures in disordered systems. We…

Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still…

Droplet condensation on surfaces produces patterns, called breath figures. Their evolution into self-similar structures is a classical example of self-organization. It is described by a scaling theory with scaling functions whose…