The characterization of holomorphic vector fields vanishing at an infinite type point

Jisoo Byun; Jae Cheon Joo; Minju Song

doi:10.1016/j.jmaa.2011.09.025

The characterization of holomorphic vector fields vanishing at an infinite type point

Jisoo Byun^*, Jae Cheon Joo, Minju Song

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

This paper consider a rotationally symmetric real hypersurface in C{double-struck}² around the origin. We also assume that the origin is a point of infinite type in the sense of D'Angelo. We prove that a holomorphic vector field defined on a neighborhood of origin which is tangent to the real hypersurface and vanishing at the origin is indeed a vector field generating rotational transformations.

Original language	English
Pages (from-to)	667-675
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	387
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.09.025
State	Published - 15 Mar 2012
Externally published	Yes

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (J. Byun), [email protected] (J.-C. Joo), [email protected] (M. Song). 1 Jisoo Byun’s research was supported by Basic Science Research Program through the National Research Foundation Ministry of Education, Science and Technology (2010-0003702).

Funding Information:
of Korea (NRF) funded by the

Keywords

Greene-Krantz conjecture
Holomorphic vector fields

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2011.09.025

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title = "The characterization of holomorphic vector fields vanishing at an infinite type point",

abstract = "This paper consider a rotationally symmetric real hypersurface in C\{double-struck\}2 around the origin. We also assume that the origin is a point of infinite type in the sense of D'Angelo. We prove that a holomorphic vector field defined on a neighborhood of origin which is tangent to the real hypersurface and vanishing at the origin is indeed a vector field generating rotational transformations.",

keywords = "Greene-Krantz conjecture, Holomorphic vector fields",

author = "Jisoo Byun and Joo, \{Jae Cheon\} and Minju Song",

note = "Funding Information: E-mail addresses: [email protected] (J. Byun), [email protected] (J.-C. Joo), [email protected] (M. Song). 1 Jisoo Byun{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation Ministry of Education, Science and Technology (2010-0003702). Funding Information: of Korea (NRF) funded by the",

year = "2012",

month = mar,

day = "15",

doi = "10.1016/j.jmaa.2011.09.025",

language = "English",

volume = "387",

pages = "667--675",

journal = "Journal of Mathematical Analysis and Applications",

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T1 - The characterization of holomorphic vector fields vanishing at an infinite type point

AU - Byun, Jisoo

AU - Joo, Jae Cheon

AU - Song, Minju

N1 - Funding Information: E-mail addresses: [email protected] (J. Byun), [email protected] (J.-C. Joo), [email protected] (M. Song). 1 Jisoo Byun’s research was supported by Basic Science Research Program through the National Research Foundation Ministry of Education, Science and Technology (2010-0003702). Funding Information: of Korea (NRF) funded by the

PY - 2012/3/15

Y1 - 2012/3/15

N2 - This paper consider a rotationally symmetric real hypersurface in C{double-struck}2 around the origin. We also assume that the origin is a point of infinite type in the sense of D'Angelo. We prove that a holomorphic vector field defined on a neighborhood of origin which is tangent to the real hypersurface and vanishing at the origin is indeed a vector field generating rotational transformations.

AB - This paper consider a rotationally symmetric real hypersurface in C{double-struck}2 around the origin. We also assume that the origin is a point of infinite type in the sense of D'Angelo. We prove that a holomorphic vector field defined on a neighborhood of origin which is tangent to the real hypersurface and vanishing at the origin is indeed a vector field generating rotational transformations.

KW - Greene-Krantz conjecture

KW - Holomorphic vector fields

UR - https://www.scopus.com/pages/publications/80255137488

U2 - 10.1016/j.jmaa.2011.09.025

DO - 10.1016/j.jmaa.2011.09.025

M3 - Article

AN - SCOPUS:80255137488

SN - 0022-247X

VL - 387

SP - 667

EP - 675

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

The characterization of holomorphic vector fields vanishing at an infinite type point

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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