Compactness of Alexandrov-Nirenberg Surfaces

We study a class of compact surfaces in R-3 introduced by Alexandrov and generalized by Nirenberg and prove a compactness result under suitable assumptions on induced metrics and Gauss curvatures. (c) 2017 Wiley Periodicals, Inc.National Science Foundation [DMS-140459]; National Natural Science Foundation of China [11121101, 11131005]SCI(E)ARTICLE91706-17537