Related papers: An Improved Energy-Area Inequality for Harmonic Ma…
The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this…
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…
In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…
As noticed in Ref.[1], the Ore-Powell's classical calculation of the o-Ps -> 3 gamma decay amplitude does not fulfill Low's theorem requirements for the low energy end of the photon spectrum. We reanalyze the implications of Low's theorem…
We establish some new results about the $\Gamma$-limit, with respect to the $L^1$-topology, of two different (but related) phase-field approximations of the so-called Euler's Elastica Bending Energy for curves in the plane.
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
In this paper, we prove the boundary partial regularity for a class of coupled Dirac-harmonic maps satisfying a certain energy monotonicity inequality near the boundary.
We give curvature-dependant convergence rates for the optimization of weakly convex functions defined on a manifold of 1-bounded geometry via Riemannian gradient descent and via the dynamic trivialization algorithm. In order to do this, we…
We try to retrieve the power spectra with certainty to the highest spatial frequencies allowed by current instrumentation. For this, we use 2D inversion code that were able to recover information up to the instrumental diffraction limit.…
We study analytic properties of harmonic maps from Riemannian polyhedra into CAT($\kappa$) spaces for $\kappa\in\{0,1\}$. Locally, on each top-dimensional face of the domain, this amounts to studying harmonic maps from smooth domains into…
For degree $\pm 1$ harmonic maps from $\mathbb{R}^2$ (or $\mathbb{S}^2$) to $\mathbb{S}^2$, Bernand-Mantel, Muratov and Simon \cite{bernand2021quantitative} recently establish a uniformly quantitative stability estimate. Namely, for any map…
In this tutorial, we combine the different scientific fields of information theory, thermodynamics, regularization theory and non-destructive imaging, especially for photoacoustic and photothermal imaging. The goal is to get a better…
No imaging apparatus can produce perfect images: spatial resolution is limited by the Rayleigh diffraction bound that is a consequence of the imager's finite spatial extent. We show some N-photon strategies that permit resolution of details…
Image retargeting, which resizes images to one with a prescribed aspect ratio by determining an optimal warping map, has gained substantial interest in imaging science. Despite significant advances, existing methods often fail to ensure…
We study several geometric and analytic aspects of Dirac-harmonic maps with curvature term from closed Riemannian surfaces.
The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power…
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…
This is primarily a survey of the developments in the theory of harmonic maps of finite uniton number (or unitons) which have taken place since the introduction of extended solutions by Uhlenbeck. Such maps include all harmonic maps from…
In this paper we study 1-equivariant wave maps of finite energy from 1+3-dimensional Minkowski space exterior to the unit ball at the origin into the 3-sphere. We impose a Dirichlet boundary condition at r=1, meaning that the unit sphere in…