4 papers
Non-constancy and multiplicity of half-harmonic maps from intervals into the circle
Ali Hyder, Luca Martinazzi
We study one-dimensional half-harmonic maps from the real line into the circle with prescribed exterior data. We show that, for every positive integer , if two disjoint interval…
Bol's type inequality for singular metrics and its application to prescribing -curvature problems
Mrityunjoy Ghosh, Ali Hyder
In this article, we study higher-order Bol's inequality for radial normal solutions to a singular Liouville equation. By applying these inequalities along with compactness argument…
One-dimensional half-harmonic maps into the circle and their degree
Luca Martinazzi, Ali Hyder
Given a half-harmonic map minimizing the fractional Dirichlet energy under Dirichlet boundary conditions in $\mathbb{R}\setmi…
The limiting case of the fractional Caffarelli-Kohn-Nirenberg inequality in dimension one
Maria del Mar Gonzalez, Ali Hyder, Mariel Saez
In this paper we study the fractional Caffarelli-Kohn-Nirenberg inequality (CKN) in one dimension when the parameter converges (from the left) to its critical value , obt…