arXiv subjects

Francesc Alcover

Publications and source records attributed to Francesc Alcover.

3 recordsLinked to original sources

arXiv2026

Periodic Delaunay cylinders with constant anisotropic nonlocal mean curvature

In this article we prove existence and symmetry properties of periodic surfaces of revolution with constant anisotropic nonlocal mean curvature, generalizing a classical result of Delaunay to the anisotropic nonlocal setting. First, by studying the corresponding periodic isoperimetric problem, under natural assumptions on the kernel, we use rearrangement inequalities to extend a periodic version of the Wulff inequality to the nonlocal setting. This leads to the existence and symmetry properties of minimizers for every given volume in each period, thus generalizing the results of Cabr\'e, Csat\'o, and Mas to the anisotropic case. Second, under the same hypotheses on the kernel, we prove the existence of a one-parameter family of Delaunay near-cylinders in $\mathbb{R}^2$ bifurcating from a straight cylinder and having each constant anisotropic mean curvature. This extends the results of Cabr\'e, Fall, Sol\`a-Morales, and Weth to the anisotropic case. The stability of these near-cylinders will be studied in a forthcoming paper.

math.AP↗

arXiv2025

Super-Resolution of Sentinel-2 Images Using a Geometry-Guided Back-Projection Network with Self-Attention

The Sentinel-2 mission provides multispectral imagery with 13 bands at resolutions of 10m, 20m, and 60m. In particular, the 10m bands offer fine structural detail, while the 20m bands capture richer spectral information. In this paper, we propose a geometry-guided super-resolution model for fusing the 10m and 20m bands. Our approach introduces a cluster-based learning procedure to generate a geometry-rich guiding image from the 10m bands. This image is integrated into an unfolded back-projection architecture that leverages image self-similarities through a multi-head attention mechanism, which models nonlocal patch-based interactions across spatial and spectral dimensions. We also generate a dataset for evaluation, comprising three testing sets that include urban, rural, and coastal landscapes. Experimental results demonstrate that our method outperforms both classical and deep learning-based super-resolution and fusion techniques.

eess.IV↗

arXiv2025

Nonlocal BV and nonlocal Sobolev spaces induced by nonfractional weight functions

In this paper, we expand upon the theory of the space of functions with nonlocal weighted bounded variation, first introduced by Kindermann et.al. in 2005 and later generalized by Wang et.al. in 2014. We consider nonfractional C^1 weights and, using an analogous formulation to the aforementioned works, we also introduce a (to our knowledge) new class of nonlocal weighted Sobolev spaces. After establishing some fundamental properties and results regarding the structure of these spaces, we study their relationship with the classical BV and Sobolev spaces, as well as with the space of test functions. We handle both the case of domains with finite measure and that of domains of infinite measure, and show that these two situations lead to quite different scenarios. As an application, we also show that these function spaces are suitable for establishing existence and uniqueness results of global minimizers for several classes of functionals. Some of these functionals were introduced in the above-mentioned references for the study of image deblurring problems.

math.FA↗