Liouville-type theorems on the complete gradient shrinking Ricci solitons

Huabin Ge; Shijin Zhang

doi:10.1016/j.difgeo.2017.11.002

Liouville-type theorems on the complete gradient shrinking Ricci solitons

Huabin Ge
, Shijin Zhang^*

^*Corresponding author for this work

School of Mathematical Sciences

Beijing Jiaotong University

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

6 Scopus citations

Abstract

We prove that there does not exist non-constant positive f-harmonic function on the complete gradient shrinking Ricci solitons. We also prove that for any positive L^p(e^−fdV_g) f-subharmonic function for p≥1 (or f-superharmonic function for 0<p≤1) on the complete gradient shrinking Ricci soliton must be constant.

Original language	English
Pages (from-to)	42-53
Number of pages	12
Journal	Differential Geometry and its Application
Volume	56
DOIs	https://doi.org/10.1016/j.difgeo.2017.11.002
State	Published - Feb 2018

Keywords

Liouville-type theorems
Positive f-harmonic function
Shrinking gradient Ricci solitons

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10.1016/j.difgeo.2017.11.002

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title = "Liouville-type theorems on the complete gradient shrinking Ricci solitons",

abstract = "We prove that there does not exist non-constant positive f-harmonic function on the complete gradient shrinking Ricci solitons. We also prove that for any positive Lp(e−fdVg) f-subharmonic function for p≥1 (or f-superharmonic function for 0",

keywords = "Liouville-type theorems, Positive f-harmonic function, Shrinking gradient Ricci solitons",

author = "Huabin Ge and Shijin Zhang",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = feb,

doi = "10.1016/j.difgeo.2017.11.002",

language = "英语",

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AU - Ge, Huabin

AU - Zhang, Shijin

PY - 2018/2

Y1 - 2018/2

N2 - We prove that there does not exist non-constant positive f-harmonic function on the complete gradient shrinking Ricci solitons. We also prove that for any positive Lp(e−fdVg) f-subharmonic function for p≥1 (or f-superharmonic function for 0

AB - We prove that there does not exist non-constant positive f-harmonic function on the complete gradient shrinking Ricci solitons. We also prove that for any positive Lp(e−fdVg) f-subharmonic function for p≥1 (or f-superharmonic function for 0

KW - Liouville-type theorems

KW - Positive f-harmonic function

KW - Shrinking gradient Ricci solitons

UR - https://www.scopus.com/pages/publications/85034114002

U2 - 10.1016/j.difgeo.2017.11.002

DO - 10.1016/j.difgeo.2017.11.002

M3 - 文章

AN - SCOPUS:85034114002

SN - 0926-2245

VL - 56

SP - 42

EP - 53

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

ER -

Liouville-type theorems on the complete gradient shrinking Ricci solitons

Abstract

Keywords

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