2007/10/01 by Albert Clop, Clop, Albert, Ignacio Uriarte-Tuero +1
Computer Science · Mathematics · #30C62 #35J15 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.0710.0234
openalex publication_date 2007/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let α∈(0,1), K≥ 1, and d=2(1+αK)/(1+K). Given a compact set E⊂\C, it is known that if \Hd(E)=0 then E is removable for α-Hölder continuous K-quasiregular mappings in the plane. The sharpness of the index d is shown with the construction, for any t>d, of a set E of Hausdorff dimension dim(E)=t which is not removable. In this paper, we improve this result and construct compact nonremovable sets E such that 0