Quasiconformal, Lipschitz, and BV mappings in metric spaces

2022/04/27 by Lahti, Panu
#26B30 #30L10 #46E36 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2204.12854

Abstract

Consider a mapping f\colon X→ Y between two metric measure spaces. We study generalized versions of the local Lipschitz number Lip f, as well as of the distortion number H_f that is used to define quasiconformal mappings. Using these, we give sufficient conditions for f being a BV mapping f∈ BV_loc(X;Y) or a Newton-Sobolev mapping f∈ N_loc^1,p(X;Y), with 1≤ p

Related

• Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces
• Generalized Lipschitz numbers, fine differentiability, and quasiconformal mappings
• Quasiconformal curves and quasiconformal maps in metric spaces
• Geometric and analytic quasiconformality in metric measure spaces
• Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces