On 1/2 estimate for global Newlander–Nirenberg theorem: On 1/2 estimate for global Newlander–Nirenberg theorem: Z. Shi.

Given a formally integrable almost complex structure J defined on the closure of a bounded domain D ⊂ C n , and provided that J is sufficiently close to the standard complex structure, the global Newlander–Nirenberg problem asks whether there exists a global diffeomorphism defined on D ¯ that transforms J into the standard complex structure, under certain geometric and regularity assumptions on D. In this paper we prove a quantitative result of this problem. Assuming D is a strictly pseudoconvex domain in C n with C 2 boundary, and that the almost complex structure J belongs to the Hölder–Zygmund class Λ r (D ¯) for r > 3 2 , we show the existence of a global diffeomorphism (independent of r) in the class Λ r + 1 2 - ε (D ¯) , for any ε > 0 . [ABSTRACT FROM AUTHOR]