Li, HaizhongXiong, Changwei2021-04-281050-6926http://hdl.handle.net/1885/231083In this paper we provide a pinching condition for the characterization of the totally geodesic disk and the rotational annulus among minimal surfaces with free boundary in geodesic balls of three-dimensional hyperbolic space and hemisphere. The pinching condition involves the length of the second fundamental form, the support function of the surface, and a natural potential function in hyperbolic space and hemisphere.The first author was supported by NSFC Grant No. 11671224. The second author was supported by a postdoctoral fellowship funded via ARC Laureate Fellowship FL150100126.application/pdfen-AU© Mathematica Josephina, Inc. 2017Gap theoremMinimal surfaceFree boundaryHyperbolic spaceHemisphere201710.1007/s12220-017-9953-62020-11-23