A note on uniqueness boundary of holomorphic mappings

http://repository.vnu.edu.vn/handle/VNU_123/28829

In this paper, we prove Huang et al.'s conjecture stated that if f is a holomorphic function on Delta(+) := {z is an element of C :vertical bar z vertical bar < 1, Im(z) > 0} with C-infinity-smooth extension up to (-1, 1) such that f maps (-1, 1) into a cone Gamma(C) := {z is an element of C : vertical bar Im(z)vertical bar <= C vertical bar Re(z)|}, for some positive number C, and f vanishes to infinite order at 0, then f vanishes identically.

In addition, some regularity properties of the Riemann mapping functions on the boundary and an example concerning Huang et al.'s conjecture are also given.

Title:	A note on uniqueness boundary of holomorphic mappings
Authors:	Van Thu Ninh Nguyen Ngoc Khanh
Keywords:	Riemann mapping function infinite order; analytic cusp Primary 32H12 Secondary
Issue Date:	2017
Publisher:	TAYLOR & FRANCIS LTD, 2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
Citation:	ISIKNOWLEDGE
Abstract:	In this paper, we prove Huang et al.'s conjecture stated that if f is a holomorphic function on Delta(+) := {z is an element of C :vertical bar z vertical bar < 1, Im(z) > 0} with C-infinity-smooth extension up to (-1, 1) such that f maps (-1, 1) into a cone Gamma(C) := {z is an element of C : vertical bar Im(z)vertical bar <= C vertical bar Re(z)|}, for some positive number C, and f vanishes to infinite order at 0, then f vanishes identically. In addition, some regularity properties of the Riemann mapping functions on the boundary and an example concerning Huang et al.'s conjecture are also given.
Description:	TNS07014 ; COMPLEX VARIABLES AND ELLIPTIC EQUATIONS Volume: 62 Issue: 4 Pages: 481-493 Published: 2017
URI:	http://repository.vnu.edu.vn/handle/VNU_123/28829
ISSN:	1747-6933 1747-6941
Appears in Collections:	Bài báo của ĐHQGHN trong Web of Science