Distances between homotopy classes ofWs,p(𝕊N;𝕊N)

2016/06/08 by Haïm Brezis, Haim Brezis, Petru Mironescu +1
Computer Science · Mathematics · #Advanced Operator Algebra Research #Equivalence (formal languages) #Equivalence relation #Hausdorff distance #Hausdorff space #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Homotopy lifting property #Relation (database) #Topological and Geometric Data Analysis #math.FA

paper · pdf · doi:10.1051/cocv/2016037

openalex publication_date 2016/06/08 · arxiv created 2016/06/15 · arxiv updated 2016/06/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

We introduce an equivalence relation on W^s,p(\mathbb S^N;\mathbb S^N) involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. In some special cases we even obtain exact formulas.

Citations

• Boundary regularity and the Dirichlet problem for harmonic maps