Weighted poincaré inequality and the poisson equation

Ovidiu Munteanu; Chiung Jue Anna Sung; Jiaping Wang

doi:10.1090/tran/8291

Weighted poincaré inequality and the poisson equation

Ovidiu Munteanu, Chiung Jue Anna Sung, Jiaping Wang

Mathematics

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

1 Scopus citations

Abstract

We develop Green’s function estimates for manifolds satisfying a weighted Poincaré inequality together with a compatible lower bound on the Ricci curvature. This estimate is then applied to establish existence and sharp estimates of solutions to the Poisson equation on such manifolds. As an application, a Liouville property for finite energy holomorphic functions is proven on a class of complete Kähler manifolds. Consequently, such Kähler manifolds must be connected at infinity.

Original language	English (US)
Pages (from-to)	2167-2199
Number of pages	33
Journal	Transactions of the American Mathematical Society
Volume	374
Issue number	3
DOIs	https://doi.org/10.1090/tran/8291
State	Published - Mar 2021

Bibliographical note

Funding Information:
Received by the editors November 8, 2019, and, in revised form, August 17, 2020. 2020 Mathematics Subject Classification. Primary 58J05, 53C55; Secondary 35J05. Chiung-Jue Anna Sung is the corresponding author. The first author was partially supported by NSF grant DMS-1506220. The second author was partially supported by MOST. The third author was partially supported by NSF grant DMS-1606820.

Publisher Copyright:
© 2021 American Mathematical Society. All rights reserved.

Access

10.1090/tran/8291

OpenUrl availability

Full text

Cite this

@article{77e60f38f9e04468b12c653aa57c65da,

title = "Weighted poincar{\'e} inequality and the poisson equation",

abstract = "We develop Green{\textquoteright}s function estimates for manifolds satisfying a weighted Poincar{\'e} inequality together with a compatible lower bound on the Ricci curvature. This estimate is then applied to establish existence and sharp estimates of solutions to the Poisson equation on such manifolds. As an application, a Liouville property for finite energy holomorphic functions is proven on a class of complete K{\"a}hler manifolds. Consequently, such K{\"a}hler manifolds must be connected at infinity.",

author = "Ovidiu Munteanu and Sung, {Chiung Jue Anna} and Jiaping Wang",

note = "Funding Information: Received by the editors November 8, 2019, and, in revised form, August 17, 2020. 2020 Mathematics Subject Classification. Primary 58J05, 53C55; Secondary 35J05. Chiung-Jue Anna Sung is the corresponding author. The first author was partially supported by NSF grant DMS-1506220. The second author was partially supported by MOST. The third author was partially supported by NSF grant DMS-1606820. Publisher Copyright: {\textcopyright} 2021 American Mathematical Society. All rights reserved.",

year = "2021",

month = mar,

doi = "10.1090/tran/8291",

language = "English (US)",

volume = "374",

pages = "2167--2199",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - Weighted poincaré inequality and the poisson equation

AU - Munteanu, Ovidiu

AU - Sung, Chiung Jue Anna

AU - Wang, Jiaping

N1 - Funding Information: Received by the editors November 8, 2019, and, in revised form, August 17, 2020. 2020 Mathematics Subject Classification. Primary 58J05, 53C55; Secondary 35J05. Chiung-Jue Anna Sung is the corresponding author. The first author was partially supported by NSF grant DMS-1506220. The second author was partially supported by MOST. The third author was partially supported by NSF grant DMS-1606820. Publisher Copyright: © 2021 American Mathematical Society. All rights reserved.

PY - 2021/3

Y1 - 2021/3

N2 - We develop Green’s function estimates for manifolds satisfying a weighted Poincaré inequality together with a compatible lower bound on the Ricci curvature. This estimate is then applied to establish existence and sharp estimates of solutions to the Poisson equation on such manifolds. As an application, a Liouville property for finite energy holomorphic functions is proven on a class of complete Kähler manifolds. Consequently, such Kähler manifolds must be connected at infinity.

AB - We develop Green’s function estimates for manifolds satisfying a weighted Poincaré inequality together with a compatible lower bound on the Ricci curvature. This estimate is then applied to establish existence and sharp estimates of solutions to the Poisson equation on such manifolds. As an application, a Liouville property for finite energy holomorphic functions is proven on a class of complete Kähler manifolds. Consequently, such Kähler manifolds must be connected at infinity.

UR - http://www.scopus.com/inward/record.url?scp=85101592663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85101592663&partnerID=8YFLogxK

U2 - 10.1090/tran/8291

DO - 10.1090/tran/8291

M3 - Article

AN - SCOPUS:85101592663

SN - 0002-9947

VL - 374

SP - 2167

EP - 2199

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 3

ER -

Weighted poincaré inequality and the poisson equation

Abstract

Bibliographical note

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this