Holomorphic functions on Kähler-Ricci solitons

Ovidiu Munteanu; Jiaping Wang

doi:10.1112/jlms/jdt078

Holomorphic functions on Kähler-Ricci solitons

Ovidiu Munteanu, Jiaping Wang

School of Mathematics

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

10 Scopus citations

Abstract

We establish Liouville-type results on complete Kähler manifolds admitting a real holomorphic gradient vector field. As an application, we conclude that a bounded holomorphic function on a shrinking gradient Kähler-Ricci soliton must be constant, and more generally, the dimension of the space of holomorphic functions with fixed polynomial growth order is finite and bounded by the growth order.

Original language	English (US)
Pages (from-to)	817-831
Number of pages	15
Journal	Journal of the London Mathematical Society
Volume	89
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jdt078
State	Published - Jun 2014

Bibliographical note

Funding Information:
by NSF grant No. DMS-1262140 and the second author by NSF

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10.1112/jlms/jdt078

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title = "Holomorphic functions on K{\"a}hler-Ricci solitons",

abstract = "We establish Liouville-type results on complete K{\"a}hler manifolds admitting a real holomorphic gradient vector field. As an application, we conclude that a bounded holomorphic function on a shrinking gradient K{\"a}hler-Ricci soliton must be constant, and more generally, the dimension of the space of holomorphic functions with fixed polynomial growth order is finite and bounded by the growth order.",

author = "Ovidiu Munteanu and Jiaping Wang",

note = "Funding Information: by NSF grant No. DMS-1262140 and the second author by NSF",

year = "2014",

month = jun,

doi = "10.1112/jlms/jdt078",

language = "English (US)",

volume = "89",

pages = "817--831",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "John Wiley and Sons Ltd",

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T1 - Holomorphic functions on Kähler-Ricci solitons

AU - Munteanu, Ovidiu

AU - Wang, Jiaping

N1 - Funding Information: by NSF grant No. DMS-1262140 and the second author by NSF

PY - 2014/6

Y1 - 2014/6

N2 - We establish Liouville-type results on complete Kähler manifolds admitting a real holomorphic gradient vector field. As an application, we conclude that a bounded holomorphic function on a shrinking gradient Kähler-Ricci soliton must be constant, and more generally, the dimension of the space of holomorphic functions with fixed polynomial growth order is finite and bounded by the growth order.

AB - We establish Liouville-type results on complete Kähler manifolds admitting a real holomorphic gradient vector field. As an application, we conclude that a bounded holomorphic function on a shrinking gradient Kähler-Ricci soliton must be constant, and more generally, the dimension of the space of holomorphic functions with fixed polynomial growth order is finite and bounded by the growth order.

UR - https://www.scopus.com/pages/publications/84901985980

UR - https://www.scopus.com/inward/citedby.url?scp=84901985980&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdt078

DO - 10.1112/jlms/jdt078

M3 - Article

AN - SCOPUS:84901985980

SN - 0024-6107

VL - 89

SP - 817

EP - 831

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -

Holomorphic functions on Kähler-Ricci solitons

Abstract

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